information sharing between vertical hierarchies · ) interaction between information exchange...
TRANSCRIPT
![Page 1: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/1.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Information Sharingbetween Vertical Hierarchies
Marco Pagnozzi Salvatore Piccolo
September 2012
![Page 2: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/2.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Introduction
Why do competitors share private information?
The essence of an organization is based on the trade-o¤between the costs and bene�ts of communication amongits members (Arrow)
Information sharing agreements are widespread:
Banks exchange information about borrowersSellers share information about consumers�demandFirms disclose information about management�s performance
![Page 3: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/3.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Introduction
Why do competitors share private information?
The essence of an organization is based on the trade-o¤between the costs and bene�ts of communication amongits members (Arrow)
Information sharing agreements are widespread:
Banks exchange information about borrowersSellers share information about consumers�demandFirms disclose information about management�s performance
![Page 4: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/4.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Introduction
Why do competitors share private information?
The essence of an organization is based on the trade-o¤between the costs and bene�ts of communication amongits members (Arrow)
Information sharing agreements are widespread:
Banks exchange information about borrowers
Sellers share information about consumers�demandFirms disclose information about management�s performance
![Page 5: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/5.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Introduction
Why do competitors share private information?
The essence of an organization is based on the trade-o¤between the costs and bene�ts of communication amongits members (Arrow)
Information sharing agreements are widespread:
Banks exchange information about borrowersSellers share information about consumers�demand
Firms disclose information about management�s performance
![Page 6: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/6.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Introduction
Why do competitors share private information?
The essence of an organization is based on the trade-o¤between the costs and bene�ts of communication amongits members (Arrow)
Information sharing agreements are widespread:
Banks exchange information about borrowersSellers share information about consumers�demandFirms disclose information about management�s performance
![Page 7: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/7.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Literature
IO: information sharing can increase e¢ ciency or reducecompetition � e.g., Novshek and Sonnenschein (1982),Clarke (1983), Vives (1984) ...
Banking: lenders exchange information to screen investmentprojects or discipline borrowers � e.g., Pagano and Jappelli(1993) ...
Consumers�privacy: sellers use information on consumers toprice discriminate � Acquisti and Varian (2005), Taylor(2004)
... But these papers neglect the source of information
Ganuza and Jansen (2012) show how information sharinga¤ects �rms�incentive to acquire signals about their costs
![Page 8: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/8.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Literature
IO: information sharing can increase e¢ ciency or reducecompetition � e.g., Novshek and Sonnenschein (1982),Clarke (1983), Vives (1984) ...
Banking: lenders exchange information to screen investmentprojects or discipline borrowers � e.g., Pagano and Jappelli(1993) ...
Consumers�privacy: sellers use information on consumers toprice discriminate � Acquisti and Varian (2005), Taylor(2004)
... But these papers neglect the source of information
Ganuza and Jansen (2012) show how information sharinga¤ects �rms�incentive to acquire signals about their costs
![Page 9: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/9.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Literature
IO: information sharing can increase e¢ ciency or reducecompetition � e.g., Novshek and Sonnenschein (1982),Clarke (1983), Vives (1984) ...
Banking: lenders exchange information to screen investmentprojects or discipline borrowers � e.g., Pagano and Jappelli(1993) ...
Consumers�privacy: sellers use information on consumers toprice discriminate � Acquisti and Varian (2005), Taylor(2004)
... But these papers neglect the source of information
Ganuza and Jansen (2012) show how information sharinga¤ects �rms�incentive to acquire signals about their costs
![Page 10: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/10.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Literature
IO: information sharing can increase e¢ ciency or reducecompetition � e.g., Novshek and Sonnenschein (1982),Clarke (1983), Vives (1984) ...
Banking: lenders exchange information to screen investmentprojects or discipline borrowers � e.g., Pagano and Jappelli(1993) ...
Consumers�privacy: sellers use information on consumers toprice discriminate � Acquisti and Varian (2005), Taylor(2004)
... But these papers neglect the source of information
Ganuza and Jansen (2012) show how information sharinga¤ects �rms�incentive to acquire signals about their costs
![Page 11: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/11.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Literature
IO: information sharing can increase e¢ ciency or reducecompetition � e.g., Novshek and Sonnenschein (1982),Clarke (1983), Vives (1984) ...
Banking: lenders exchange information to screen investmentprojects or discipline borrowers � e.g., Pagano and Jappelli(1993) ...
Consumers�privacy: sellers use information on consumers toprice discriminate � Acquisti and Varian (2005), Taylor(2004)
... But these papers neglect the source of information
Ganuza and Jansen (2012) show how information sharinga¤ects �rms�incentive to acquire signals about their costs
![Page 12: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/12.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Contribution
Principals obtain information through contracting withexclusive and privately informed agents
Principals compete and may share information
) Interaction between information exchange acrossorganizations and agency con�icts within organizations
e.g.: Two competing manufacturers that sell through privatelyinformed retailers and may share the information obtainedfrom them
Link between information sharing and vertical contracting:Calzolari and Pavan (2006) analyze information transmissionin sequential common agency
![Page 13: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/13.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Contribution
Principals obtain information through contracting withexclusive and privately informed agents
Principals compete and may share information
) Interaction between information exchange acrossorganizations and agency con�icts within organizations
e.g.: Two competing manufacturers that sell through privatelyinformed retailers and may share the information obtainedfrom them
Link between information sharing and vertical contracting:Calzolari and Pavan (2006) analyze information transmissionin sequential common agency
![Page 14: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/14.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Contribution
Principals obtain information through contracting withexclusive and privately informed agents
Principals compete and may share information
) Interaction between information exchange acrossorganizations and agency con�icts within organizations
e.g.: Two competing manufacturers that sell through privatelyinformed retailers and may share the information obtainedfrom them
Link between information sharing and vertical contracting:Calzolari and Pavan (2006) analyze information transmissionin sequential common agency
![Page 15: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/15.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Contribution
Principals obtain information through contracting withexclusive and privately informed agents
Principals compete and may share information
) Interaction between information exchange acrossorganizations and agency con�icts within organizations
e.g.: Two competing manufacturers that sell through privatelyinformed retailers and may share the information obtainedfrom them
Link between information sharing and vertical contracting:Calzolari and Pavan (2006) analyze information transmissionin sequential common agency
![Page 16: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/16.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Contribution
Principals obtain information through contracting withexclusive and privately informed agents
Principals compete and may share information
) Interaction between information exchange acrossorganizations and agency con�icts within organizations
e.g.: Two competing manufacturers that sell through privatelyinformed retailers and may share the information obtainedfrom them
Link between information sharing and vertical contracting:Calzolari and Pavan (2006) analyze information transmissionin sequential common agency
![Page 17: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/17.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Result
Information sharing a¤ects principals�incentiveto distort agents�output to extract rents
The choice to share information only depends on:
the nature of competition between principals andthe correlation of agents�information
) Principals share information i¤ externalities and correlationhave the same sign
This e¤ect is of �rst-order relative to thosewith complete information
Principals face a prisoner�s dilemmawhen they do not share information
![Page 18: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/18.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Result
Information sharing a¤ects principals�incentiveto distort agents�output to extract rents
The choice to share information only depends on:
the nature of competition between principals andthe correlation of agents�information
) Principals share information i¤ externalities and correlationhave the same sign
This e¤ect is of �rst-order relative to thosewith complete information
Principals face a prisoner�s dilemmawhen they do not share information
![Page 19: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/19.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Result
Information sharing a¤ects principals�incentiveto distort agents�output to extract rents
The choice to share information only depends on:
the nature of competition between principals and
the correlation of agents�information
) Principals share information i¤ externalities and correlationhave the same sign
This e¤ect is of �rst-order relative to thosewith complete information
Principals face a prisoner�s dilemmawhen they do not share information
![Page 20: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/20.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Result
Information sharing a¤ects principals�incentiveto distort agents�output to extract rents
The choice to share information only depends on:
the nature of competition between principals andthe correlation of agents�information
) Principals share information i¤ externalities and correlationhave the same sign
This e¤ect is of �rst-order relative to thosewith complete information
Principals face a prisoner�s dilemmawhen they do not share information
![Page 21: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/21.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Result
Information sharing a¤ects principals�incentiveto distort agents�output to extract rents
The choice to share information only depends on:
the nature of competition between principals andthe correlation of agents�information
) Principals share information i¤ externalities and correlationhave the same sign
This e¤ect is of �rst-order relative to thosewith complete information
Principals face a prisoner�s dilemmawhen they do not share information
![Page 22: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/22.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Result
Information sharing a¤ects principals�incentiveto distort agents�output to extract rents
The choice to share information only depends on:
the nature of competition between principals andthe correlation of agents�information
) Principals share information i¤ externalities and correlationhave the same sign
This e¤ect is of �rst-order relative to thosewith complete information
Principals face a prisoner�s dilemmawhen they do not share information
![Page 23: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/23.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Result
Information sharing a¤ects principals�incentiveto distort agents�output to extract rents
The choice to share information only depends on:
the nature of competition between principals andthe correlation of agents�information
) Principals share information i¤ externalities and correlationhave the same sign
This e¤ect is of �rst-order relative to thosewith complete information
Principals face a prisoner�s dilemmawhen they do not share information
![Page 24: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/24.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Model
Two principals: P1 and P2
Two exclusive agents: A1 and A2Ai is privately informed about marginal cost θi 2
�θ, θ, with:
Pr(θ, θ) = ν2 + α; Pr(θ, θ) = (1� ν)2 + αPr(θ, θ) = Pr(θ, θ) = ν (1� ν)� α
) α measures correlation between θ1 and θ2;Pr(θ) = ν; Pr(θ) = 1� ν;
![Page 25: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/25.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Model
Two principals: P1 and P2Two exclusive agents: A1 and A2
Ai is privately informed about marginal cost θi 2�
θ, θ, with:
Pr(θ, θ) = ν2 + α; Pr(θ, θ) = (1� ν)2 + αPr(θ, θ) = Pr(θ, θ) = ν (1� ν)� α
) α measures correlation between θ1 and θ2;Pr(θ) = ν; Pr(θ) = 1� ν;
![Page 26: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/26.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Model
Two principals: P1 and P2Two exclusive agents: A1 and A2Ai is privately informed about marginal cost θi 2
�θ, θ, with:
Pr(θ, θ) = ν2 + α; Pr(θ, θ) = (1� ν)2 + αPr(θ, θ) = Pr(θ, θ) = ν (1� ν)� α
) α measures correlation between θ1 and θ2;Pr(θ) = ν; Pr(θ) = 1� ν;
![Page 27: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/27.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Model
Two principals: P1 and P2Two exclusive agents: A1 and A2Ai is privately informed about marginal cost θi 2
�θ, θ, with:
Pr(θ, θ) = ν2 + α; Pr(θ, θ) = (1� ν)2 + α
Pr(θ, θ) = Pr(θ, θ) = ν (1� ν)� α
) α measures correlation between θ1 and θ2;Pr(θ) = ν; Pr(θ) = 1� ν;
![Page 28: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/28.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Model
Two principals: P1 and P2Two exclusive agents: A1 and A2Ai is privately informed about marginal cost θi 2
�θ, θ, with:
Pr(θ, θ) = ν2 + α; Pr(θ, θ) = (1� ν)2 + αPr(θ, θ) = Pr(θ, θ) = ν (1� ν)� α
) α measures correlation between θ1 and θ2;Pr(θ) = ν; Pr(θ) = 1� ν;
![Page 29: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/29.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Model
Two principals: P1 and P2Two exclusive agents: A1 and A2Ai is privately informed about marginal cost θi 2
�θ, θ, with:
Pr(θ, θ) = ν2 + α; Pr(θ, θ) = (1� ν)2 + αPr(θ, θ) = Pr(θ, θ) = ν (1� ν)� α
) α measures correlation between θ1 and θ2;Pr(θ) = ν; Pr(θ) = 1� ν;
![Page 30: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/30.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Utilities
Pi pays ti to Ai , and Ai produces qi
Risk-neutral players:
Ai : Ui = ti � θiqi
Pi : S i (qi , qj )| {z }�κ+βqi�q2i +δqiqj
� ti
) δ measures production externalities:
strategic complementarity (δ > 0) or substitutability (δ < 0)
We assume δ small and compute expected pro�ts throughTaylor expansions
Limited liability for agents
![Page 31: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/31.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Utilities
Pi pays ti to Ai , and Ai produces qiRisk-neutral players:
Ai : Ui = ti � θiqi
Pi : S i (qi , qj )| {z }�κ+βqi�q2i +δqiqj
� ti
) δ measures production externalities:
strategic complementarity (δ > 0) or substitutability (δ < 0)
We assume δ small and compute expected pro�ts throughTaylor expansions
Limited liability for agents
![Page 32: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/32.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Utilities
Pi pays ti to Ai , and Ai produces qiRisk-neutral players:
Ai : Ui = ti � θiqi
Pi : S i (qi , qj )| {z }�κ+βqi�q2i +δqiqj
� ti
) δ measures production externalities:
strategic complementarity (δ > 0) or substitutability (δ < 0)
We assume δ small and compute expected pro�ts throughTaylor expansions
Limited liability for agents
![Page 33: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/33.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Utilities
Pi pays ti to Ai , and Ai produces qiRisk-neutral players:
Ai : Ui = ti � θiqi
Pi : S i (qi , qj )| {z }�κ+βqi�q2i +δqiqj
� ti
) δ measures production externalities:
strategic complementarity (δ > 0) or substitutability (δ < 0)
We assume δ small and compute expected pro�ts throughTaylor expansions
Limited liability for agents
![Page 34: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/34.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Utilities
Pi pays ti to Ai , and Ai produces qiRisk-neutral players:
Ai : Ui = ti � θiqi
Pi : S i (qi , qj )| {z }�κ+βqi�q2i +δqiqj
� ti
) δ measures production externalities:
strategic complementarity (δ > 0) or substitutability (δ < 0)
We assume δ small and compute expected pro�ts throughTaylor expansions
Limited liability for agents
![Page 35: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/35.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Utilities
Pi pays ti to Ai , and Ai produces qiRisk-neutral players:
Ai : Ui = ti � θiqi
Pi : S i (qi , qj )| {z }�κ+βqi�q2i +δqiqj
� ti
) δ measures production externalities:
strategic complementarity (δ > 0) or substitutability (δ < 0)
We assume δ small and compute expected pro�ts throughTaylor expansions
Limited liability for agents
![Page 36: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/36.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Contracts
θi can be learned by Pi through private contractingand by Pj through information sharing
Pi o¤ers a direct mechanism: Ai report his cost θi and
without information sharing:
fti (θi ) , qi (θi )g
with information sharing:�ti�θi , θj
�, qi�θi , θj
�
Ai�s cost can be credibly transmitted by Pi to Pj/Aj
![Page 37: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/37.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Contracts
θi can be learned by Pi through private contractingand by Pj through information sharing
Pi o¤ers a direct mechanism: Ai report his cost θi and
without information sharing:
fti (θi ) , qi (θi )g
with information sharing:�ti�θi , θj
�, qi�θi , θj
�
Ai�s cost can be credibly transmitted by Pi to Pj/Aj
![Page 38: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/38.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Contracts
θi can be learned by Pi through private contractingand by Pj through information sharing
Pi o¤ers a direct mechanism: Ai report his cost θi and
without information sharing:
fti (θi ) , qi (θi )g
with information sharing:�ti�θi , θj
�, qi�θi , θj
�
Ai�s cost can be credibly transmitted by Pi to Pj/Aj
![Page 39: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/39.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Contracts
θi can be learned by Pi through private contractingand by Pj through information sharing
Pi o¤ers a direct mechanism: Ai report his cost θi and
without information sharing:
fti (θi ) , qi (θi )g
with information sharing:�ti�θi , θj
�, qi�θi , θj
�
Ai�s cost can be credibly transmitted by Pi to Pj/Aj
![Page 40: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/40.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Contracts
θi can be learned by Pi through private contractingand by Pj through information sharing
Pi o¤ers a direct mechanism: Ai report his cost θi and
without information sharing:
fti (θi ) , qi (θi )g
with information sharing:�ti�θi , θj
�, qi�θi , θj
�
Ai�s cost can be credibly transmitted by Pi to Pj/Aj
![Page 41: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/41.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Timing
1 Principals simultaneously choose whether to commit to shareinformation
2 Ai learns θi3 Principals contract with agents4 Pi discloses her information about Ai�s cost if she hascommitted to do so
5 Agents produce and payments are made
![Page 42: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/42.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Timing
1 Principals simultaneously choose whether to commit to shareinformation
2 Ai learns θi
3 Principals contract with agents4 Pi discloses her information about Ai�s cost if she hascommitted to do so
5 Agents produce and payments are made
![Page 43: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/43.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Timing
1 Principals simultaneously choose whether to commit to shareinformation
2 Ai learns θi3 Principals contract with agents
4 Pi discloses her information about Ai�s cost if she hascommitted to do so
5 Agents produce and payments are made
![Page 44: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/44.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Timing
1 Principals simultaneously choose whether to commit to shareinformation
2 Ai learns θi3 Principals contract with agents4 Pi discloses her information about Ai�s cost if she hascommitted to do so
5 Agents produce and payments are made
![Page 45: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/45.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Timing
1 Principals simultaneously choose whether to commit to shareinformation
2 Ai learns θi3 Principals contract with agents4 Pi discloses her information about Ai�s cost if she hascommitted to do so
5 Agents produce and payments are made
![Page 46: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/46.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Complete information within each hierarchy
Standard duopoly where �rms share cost information(Shapiro, 1986)
Let si = (θi , θj ) if Pj shares information, si = θi if Pj does not
Lemma: Pi�s expected equilibrium pro�t is
V �i = κ+(Esi [q�i (si ) jθi ]| {z }
average of q�i (si )
)2+Esi [q�i (si )�Esi [q
�i (si ) jθi )jθi ]]
2| {z }variance of q�i (si )
.
and expected output is the same regardless of principals�communication decisions
) Principals maximize output volatility
![Page 47: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/47.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Complete information within each hierarchy
Standard duopoly where �rms share cost information(Shapiro, 1986)
Let si = (θi , θj ) if Pj shares information, si = θi if Pj does not
Lemma: Pi�s expected equilibrium pro�t is
V �i = κ+(Esi [q�i (si ) jθi ]| {z }
average of q�i (si )
)2+Esi [q�i (si )�Esi [q
�i (si ) jθi )jθi ]]
2| {z }variance of q�i (si )
.
and expected output is the same regardless of principals�communication decisions
) Principals maximize output volatility
![Page 48: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/48.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Complete information within each hierarchy
Standard duopoly where �rms share cost information(Shapiro, 1986)
Let si = (θi , θj ) if Pj shares information, si = θi if Pj does not
Lemma: Pi�s expected equilibrium pro�t is
V �i = κ+(Esi [q�i (si ) jθi ]| {z }
average of q�i (si )
)2+Esi [q�i (si )�Esi [q
�i (si ) jθi )jθi ]]
2| {z }variance of q�i (si )
.
and expected output is the same regardless of principals�communication decisions
) Principals maximize output volatility
![Page 49: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/49.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Complete information within each hierarchy
Standard duopoly where �rms share cost information(Shapiro, 1986)
Let si = (θi , θj ) if Pj shares information, si = θi if Pj does not
Lemma: Pi�s expected equilibrium pro�t is
V �i = κ+(Esi [q�i (si ) jθi ]| {z }
average of q�i (si )
)2+Esi [q�i (si )�Esi [q
�i (si ) jθi )jθi ]]
2| {z }variance of q�i (si )
.
and expected output is the same regardless of principals�communication decisions
) Principals maximize output volatility
![Page 50: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/50.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Complete information
Proposition: With complete information: both principalsshare information if α > �ν (1� ν); no principal shareinformation if α < �ν (1� ν)
Information sharing has a direct positive e¤ect on outputvolatility (since contracts are conditioned on more states) butIf α < 0 information sharing reduces volatility because states(θ, θ) and (θ, θ) are more likely:
e.g., if δ > 0 outputs are more similar in those states
Proposition: Principals�information sharing decisions alwaysmaximize their pro�ts
![Page 51: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/51.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Complete information
Proposition: With complete information: both principalsshare information if α > �ν (1� ν); no principal shareinformation if α < �ν (1� ν)
Information sharing has a direct positive e¤ect on outputvolatility (since contracts are conditioned on more states) but
If α < 0 information sharing reduces volatility because states(θ, θ) and (θ, θ) are more likely:
e.g., if δ > 0 outputs are more similar in those states
Proposition: Principals�information sharing decisions alwaysmaximize their pro�ts
![Page 52: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/52.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Complete information
Proposition: With complete information: both principalsshare information if α > �ν (1� ν); no principal shareinformation if α < �ν (1� ν)
Information sharing has a direct positive e¤ect on outputvolatility (since contracts are conditioned on more states) butIf α < 0 information sharing reduces volatility because states(θ, θ) and (θ, θ) are more likely:
e.g., if δ > 0 outputs are more similar in those states
Proposition: Principals�information sharing decisions alwaysmaximize their pro�ts
![Page 53: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/53.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Complete information
Proposition: With complete information: both principalsshare information if α > �ν (1� ν); no principal shareinformation if α < �ν (1� ν)
Information sharing has a direct positive e¤ect on outputvolatility (since contracts are conditioned on more states) butIf α < 0 information sharing reduces volatility because states(θ, θ) and (θ, θ) are more likely:
e.g., if δ > 0 outputs are more similar in those states
Proposition: Principals�information sharing decisions alwaysmaximize their pro�ts
![Page 54: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/54.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Complete information
Proposition: With complete information: both principalsshare information if α > �ν (1� ν); no principal shareinformation if α < �ν (1� ν)
Information sharing has a direct positive e¤ect on outputvolatility (since contracts are conditioned on more states) butIf α < 0 information sharing reduces volatility because states(θ, θ) and (θ, θ) are more likely:
e.g., if δ > 0 outputs are more similar in those states
Proposition: Principals�information sharing decisions alwaysmaximize their pro�ts
![Page 55: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/55.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Asymmetric information
Since principals learn their agents�costs through contracting,agents earn an information rent
Principals want to distort outputs to minimize rent
Principals want to a¤ect rival�s output to increase pro�t(because of externality)
3 subgames:
1 No communication2 Bilateral information sharing3 Unilateral information sharing
![Page 56: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/56.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Asymmetric information
Since principals learn their agents�costs through contracting,agents earn an information rent
Principals want to distort outputs to minimize rent
Principals want to a¤ect rival�s output to increase pro�t(because of externality)
3 subgames:
1 No communication2 Bilateral information sharing3 Unilateral information sharing
![Page 57: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/57.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Asymmetric information
Since principals learn their agents�costs through contracting,agents earn an information rent
Principals want to distort outputs to minimize rent
Principals want to a¤ect rival�s output to increase pro�t(because of externality)
3 subgames:
1 No communication2 Bilateral information sharing3 Unilateral information sharing
![Page 58: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/58.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Asymmetric information
Since principals learn their agents�costs through contracting,agents earn an information rent
Principals want to distort outputs to minimize rent
Principals want to a¤ect rival�s output to increase pro�t(because of externality)
3 subgames:
1 No communication2 Bilateral information sharing3 Unilateral information sharing
![Page 59: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/59.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Asymmetric information
Since principals learn their agents�costs through contracting,agents earn an information rent
Principals want to distort outputs to minimize rent
Principals want to a¤ect rival�s output to increase pro�t(because of externality)
3 subgames:1 No communication
2 Bilateral information sharing3 Unilateral information sharing
![Page 60: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/60.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Asymmetric information
Since principals learn their agents�costs through contracting,agents earn an information rent
Principals want to distort outputs to minimize rent
Principals want to a¤ect rival�s output to increase pro�t(because of externality)
3 subgames:1 No communication2 Bilateral information sharing
3 Unilateral information sharing
![Page 61: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/61.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Asymmetric information
Since principals learn their agents�costs through contracting,agents earn an information rent
Principals want to distort outputs to minimize rent
Principals want to a¤ect rival�s output to increase pro�t(because of externality)
3 subgames:1 No communication2 Bilateral information sharing3 Unilateral information sharing
![Page 62: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/62.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
No communication
Pi maximizes
EθjEθi [S (qi (θi ), qe (θj ))� θiqi (θi ) jθi ]� ν∆θqi (θ)
First-order conditions are
Eθ [S1 (qe (θ), qe (θj )) jθ] = θ,
Eθ
�S1(qe (θ), qe (θj ))jθ
�= θ + ν
1�ν ∆θ.
) Type θ produces the output that equalizes marginal bene�tto marginal costType θ�s output is downward distorted to reduce agents�rent
![Page 63: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/63.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
No communication
Pi maximizes
EθjEθi [S (qi (θi ), qe (θj ))� θiqi (θi ) jθi ]� ν∆θqi (θ)
First-order conditions are
Eθ [S1 (qe (θ), qe (θj )) jθ] = θ,
Eθ
�S1(qe (θ), qe (θj ))jθ
�= θ + ν
1�ν ∆θ.
) Type θ produces the output that equalizes marginal bene�tto marginal costType θ�s output is downward distorted to reduce agents�rent
![Page 64: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/64.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
No communication
Pi maximizes
EθjEθi [S (qi (θi ), qe (θj ))� θiqi (θi ) jθi ]� ν∆θqi (θ)
First-order conditions are
Eθ [S1 (qe (θ), qe (θj )) jθ] = θ,
Eθ
�S1(qe (θ), qe (θj ))jθ
�= θ + ν
1�ν ∆θ.
) Type θ produces the output that equalizes marginal bene�tto marginal costType θ�s output is downward distorted to reduce agents�rent
![Page 65: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/65.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
No communication
Proposition. When principals do not share information:
� qe (θ) < q�(θ)
� qe (θ) > q�(θ) i¤ δ < 0
Because of production externalities, the low-cost agent�soutput is distorted since principals expect rivals to produceless to reduce information rents:
If goods are substitutes (complements), Aj�s lower outputinduces Ai to produce more (less)
![Page 66: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/66.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
No communication
Proposition. When principals do not share information:� qe (θ) < q�(θ)
� qe (θ) > q�(θ) i¤ δ < 0
Because of production externalities, the low-cost agent�soutput is distorted since principals expect rivals to produceless to reduce information rents:
If goods are substitutes (complements), Aj�s lower outputinduces Ai to produce more (less)
![Page 67: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/67.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
No communication
Proposition. When principals do not share information:� qe (θ) < q�(θ)
� qe (θ) > q�(θ) i¤ δ < 0
Because of production externalities, the low-cost agent�soutput is distorted since principals expect rivals to produceless to reduce information rents:
If goods are substitutes (complements), Aj�s lower outputinduces Ai to produce more (less)
![Page 68: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/68.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
No communication
Proposition. When principals do not share information:� qe (θ) < q�(θ)
� qe (θ) > q�(θ) i¤ δ < 0
Because of production externalities, the low-cost agent�soutput is distorted since principals expect rivals to produceless to reduce information rents:
If goods are substitutes (complements), Aj�s lower outputinduces Ai to produce more (less)
![Page 69: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/69.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
No communication
Proposition. When principals do not share information:� qe (θ) < q�(θ)
� qe (θ) > q�(θ) i¤ δ < 0
Because of production externalities, the low-cost agent�soutput is distorted since principals expect rivals to produceless to reduce information rents:
If goods are substitutes (complements), Aj�s lower outputinduces Ai to produce more (less)
![Page 70: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/70.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Bilateral information sharing
Contracts specify qi and ti contingent on (θi , θj )
Relevant constraints:
Ui�θ, θj
�= ti
�θ, θj
�� θqi
�θ, θj
�� 0 8θj ,
Eθj [Ui (θ, θj ) jθ] � Eθj
�ti�θ, θj
�� θqi
�θ, θj
�jθ�
) Pi maximizes:
EθjEθi [S (qi (θi , θj ) , qe (θj , θi ))� θiqi (θi , θj ) jθi ]
� ν∆θEθj
�qi (θ, θj )jθ
�(No full surplus extraction due to limited liability)
![Page 71: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/71.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Bilateral information sharing
Contracts specify qi and ti contingent on (θi , θj )
Relevant constraints:
Ui�θ, θj
�= ti
�θ, θj
�� θqi
�θ, θj
�� 0 8θj ,
Eθj [Ui (θ, θj ) jθ] � Eθj
�ti�θ, θj
�� θqi
�θ, θj
�jθ�
) Pi maximizes:
EθjEθi [S (qi (θi , θj ) , qe (θj , θi ))� θiqi (θi , θj ) jθi ]
� ν∆θEθj
�qi (θ, θj )jθ
�(No full surplus extraction due to limited liability)
![Page 72: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/72.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Bilateral information sharing
Contracts specify qi and ti contingent on (θi , θj )
Relevant constraints:
Ui�θ, θj
�= ti
�θ, θj
�� θqi
�θ, θj
�� 0 8θj ,
Eθj [Ui (θ, θj ) jθ] � Eθj
�ti�θ, θj
�� θqi
�θ, θj
�jθ�
) Pi maximizes:
EθjEθi [S (qi (θi , θj ) , qe (θj , θi ))� θiqi (θi , θj ) jθi ]
� ν∆θEθj
�qi (θ, θj )jθ
�
(No full surplus extraction due to limited liability)
![Page 73: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/73.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Bilateral information sharing
Contracts specify qi and ti contingent on (θi , θj )
Relevant constraints:
Ui�θ, θj
�= ti
�θ, θj
�� θqi
�θ, θj
�� 0 8θj ,
Eθj [Ui (θ, θj ) jθ] � Eθj
�ti�θ, θj
�� θqi
�θ, θj
�jθ�
) Pi maximizes:
EθjEθi [S (qi (θi , θj ) , qe (θj , θi ))� θiqi (θi , θj ) jθi ]
� ν∆θEθj
�qi (θ, θj )jθ
�(No full surplus extraction due to limited liability)
![Page 74: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/74.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Bilateral information sharing
Necessary and su¢ cient �rst-order conditions:
S1 (qe (θ, θj ), qe (θj , θ)) = θ 8θj ,
S1(qe (θ, θj ), qe (θj , θ)) = θ + ν1�ν
Pr(θj jθ)Pr(θj jθ)
∆θ 8θj
) No distortion for θ and downward distortionfor θ to reduce information rentsDistortion increases with Pr(θj jθ)
Pr(θj jθ)since:
Pr�θj jθ
�measures how often Pi pays rent to type θ
Pr(θj jθ) measures how often output is ine¢ cient
Pr(θjθ)Pr(θjθ) >
Pr(θjθ)Pr(θjθ) , α > 0,
) if costs are positively correlated, the distortion of type θ�soutput is larger when his opponent has a low rather than ahigh cost, since this is more likely
![Page 75: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/75.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Bilateral information sharing
Necessary and su¢ cient �rst-order conditions:
S1 (qe (θ, θj ), qe (θj , θ)) = θ 8θj ,
S1(qe (θ, θj ), qe (θj , θ)) = θ + ν1�ν
Pr(θj jθ)Pr(θj jθ)
∆θ 8θj
) No distortion for θ and downward distortionfor θ to reduce information rents
Distortion increases with Pr(θj jθ)Pr(θj jθ)
since:
Pr�θj jθ
�measures how often Pi pays rent to type θ
Pr(θj jθ) measures how often output is ine¢ cient
Pr(θjθ)Pr(θjθ) >
Pr(θjθ)Pr(θjθ) , α > 0,
) if costs are positively correlated, the distortion of type θ�soutput is larger when his opponent has a low rather than ahigh cost, since this is more likely
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Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Bilateral information sharing
Necessary and su¢ cient �rst-order conditions:
S1 (qe (θ, θj ), qe (θj , θ)) = θ 8θj ,
S1(qe (θ, θj ), qe (θj , θ)) = θ + ν1�ν
Pr(θj jθ)Pr(θj jθ)
∆θ 8θj
) No distortion for θ and downward distortionfor θ to reduce information rentsDistortion increases with Pr(θj jθ)
Pr(θj jθ)since:
Pr�θj jθ
�measures how often Pi pays rent to type θ
Pr(θj jθ) measures how often output is ine¢ cient
Pr(θjθ)Pr(θjθ) >
Pr(θjθ)Pr(θjθ) , α > 0,
) if costs are positively correlated, the distortion of type θ�soutput is larger when his opponent has a low rather than ahigh cost, since this is more likely
![Page 77: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/77.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Bilateral information sharing
Necessary and su¢ cient �rst-order conditions:
S1 (qe (θ, θj ), qe (θj , θ)) = θ 8θj ,
S1(qe (θ, θj ), qe (θj , θ)) = θ + ν1�ν
Pr(θj jθ)Pr(θj jθ)
∆θ 8θj
) No distortion for θ and downward distortionfor θ to reduce information rentsDistortion increases with Pr(θj jθ)
Pr(θj jθ)since:
Pr�θj jθ
�measures how often Pi pays rent to type θ
Pr(θj jθ) measures how often output is ine¢ cient
Pr(θjθ)Pr(θjθ) >
Pr(θjθ)Pr(θjθ) , α > 0,
) if costs are positively correlated, the distortion of type θ�soutput is larger when his opponent has a low rather than ahigh cost, since this is more likely
![Page 78: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/78.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Bilateral information sharing
Necessary and su¢ cient �rst-order conditions:
S1 (qe (θ, θj ), qe (θj , θ)) = θ 8θj ,
S1(qe (θ, θj ), qe (θj , θ)) = θ + ν1�ν
Pr(θj jθ)Pr(θj jθ)
∆θ 8θj
) No distortion for θ and downward distortionfor θ to reduce information rentsDistortion increases with Pr(θj jθ)
Pr(θj jθ)since:
Pr�θj jθ
�measures how often Pi pays rent to type θ
Pr(θj jθ) measures how often output is ine¢ cient
Pr(θjθ)Pr(θjθ) >
Pr(θjθ)Pr(θjθ) , α > 0,
) if costs are positively correlated, the distortion of type θ�soutput is larger when his opponent has a low rather than ahigh cost, since this is more likely
![Page 79: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/79.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Bilateral information sharing
Necessary and su¢ cient �rst-order conditions:
S1 (qe (θ, θj ), qe (θj , θ)) = θ 8θj ,
S1(qe (θ, θj ), qe (θj , θ)) = θ + ν1�ν
Pr(θj jθ)Pr(θj jθ)
∆θ 8θj
) No distortion for θ and downward distortionfor θ to reduce information rentsDistortion increases with Pr(θj jθ)
Pr(θj jθ)since:
Pr�θj jθ
�measures how often Pi pays rent to type θ
Pr(θj jθ) measures how often output is ine¢ cient
Pr(θjθ)Pr(θjθ) >
Pr(θjθ)Pr(θjθ) , α > 0,
) if costs are positively correlated, the distortion of type θ�soutput is larger when his opponent has a low rather than ahigh cost, since this is more likely
![Page 80: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/80.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Bilateral information sharing
Proposition. If both principals share information,
qe (θ, θ) = q�(θ, θ)qe (θ, θj ) < q�(θ, θj ) 8θjqe (θ, θ) > q�(θ, θ) i¤ δ < 0Expected output does not depend on principals�communication decision
The output of type θ is ine¢ ciently low
Because of production externality, this induces Pi to alsodistort the output of type θ when θj = θ:
if δ > 0, qe (θ, θ) is lower since Pi wants to produce lesswhen Pj produces lessif δ < 0, qe (θ, θ) is higher since Pi wants to produce morewhen Pj produces less
) Strategic linkage between Pi�s output and Aj�s cost
![Page 81: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/81.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Bilateral information sharing
Proposition. If both principals share information,
qe (θ, θ) = q�(θ, θ)
qe (θ, θj ) < q�(θ, θj ) 8θjqe (θ, θ) > q�(θ, θ) i¤ δ < 0Expected output does not depend on principals�communication decision
The output of type θ is ine¢ ciently low
Because of production externality, this induces Pi to alsodistort the output of type θ when θj = θ:
if δ > 0, qe (θ, θ) is lower since Pi wants to produce lesswhen Pj produces lessif δ < 0, qe (θ, θ) is higher since Pi wants to produce morewhen Pj produces less
) Strategic linkage between Pi�s output and Aj�s cost
![Page 82: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/82.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Bilateral information sharing
Proposition. If both principals share information,
qe (θ, θ) = q�(θ, θ)qe (θ, θj ) < q�(θ, θj ) 8θj
qe (θ, θ) > q�(θ, θ) i¤ δ < 0Expected output does not depend on principals�communication decision
The output of type θ is ine¢ ciently low
Because of production externality, this induces Pi to alsodistort the output of type θ when θj = θ:
if δ > 0, qe (θ, θ) is lower since Pi wants to produce lesswhen Pj produces lessif δ < 0, qe (θ, θ) is higher since Pi wants to produce morewhen Pj produces less
) Strategic linkage between Pi�s output and Aj�s cost
![Page 83: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/83.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Bilateral information sharing
Proposition. If both principals share information,
qe (θ, θ) = q�(θ, θ)qe (θ, θj ) < q�(θ, θj ) 8θjqe (θ, θ) > q�(θ, θ) i¤ δ < 0
Expected output does not depend on principals�communication decision
The output of type θ is ine¢ ciently low
Because of production externality, this induces Pi to alsodistort the output of type θ when θj = θ:
if δ > 0, qe (θ, θ) is lower since Pi wants to produce lesswhen Pj produces lessif δ < 0, qe (θ, θ) is higher since Pi wants to produce morewhen Pj produces less
) Strategic linkage between Pi�s output and Aj�s cost
![Page 84: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/84.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Bilateral information sharing
Proposition. If both principals share information,
qe (θ, θ) = q�(θ, θ)qe (θ, θj ) < q�(θ, θj ) 8θjqe (θ, θ) > q�(θ, θ) i¤ δ < 0Expected output does not depend on principals�communication decision
The output of type θ is ine¢ ciently low
Because of production externality, this induces Pi to alsodistort the output of type θ when θj = θ:
if δ > 0, qe (θ, θ) is lower since Pi wants to produce lesswhen Pj produces lessif δ < 0, qe (θ, θ) is higher since Pi wants to produce morewhen Pj produces less
) Strategic linkage between Pi�s output and Aj�s cost
![Page 85: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/85.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Bilateral information sharing
Proposition. If both principals share information,
qe (θ, θ) = q�(θ, θ)qe (θ, θj ) < q�(θ, θj ) 8θjqe (θ, θ) > q�(θ, θ) i¤ δ < 0Expected output does not depend on principals�communication decision
The output of type θ is ine¢ ciently low
Because of production externality, this induces Pi to alsodistort the output of type θ when θj = θ:
if δ > 0, qe (θ, θ) is lower since Pi wants to produce lesswhen Pj produces lessif δ < 0, qe (θ, θ) is higher since Pi wants to produce morewhen Pj produces less
) Strategic linkage between Pi�s output and Aj�s cost
![Page 86: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/86.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Bilateral information sharing
Proposition. If both principals share information,
qe (θ, θ) = q�(θ, θ)qe (θ, θj ) < q�(θ, θj ) 8θjqe (θ, θ) > q�(θ, θ) i¤ δ < 0Expected output does not depend on principals�communication decision
The output of type θ is ine¢ ciently low
Because of production externality, this induces Pi to alsodistort the output of type θ when θj = θ:
if δ > 0, qe (θ, θ) is lower since Pi wants to produce lesswhen Pj produces lessif δ < 0, qe (θ, θ) is higher since Pi wants to produce morewhen Pj produces less
) Strategic linkage between Pi�s output and Aj�s cost
![Page 87: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/87.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Bilateral information sharing
Proposition. If both principals share information,
qe (θ, θ) = q�(θ, θ)qe (θ, θj ) < q�(θ, θj ) 8θjqe (θ, θ) > q�(θ, θ) i¤ δ < 0Expected output does not depend on principals�communication decision
The output of type θ is ine¢ ciently low
Because of production externality, this induces Pi to alsodistort the output of type θ when θj = θ:
if δ > 0, qe (θ, θ) is lower since Pi wants to produce lesswhen Pj produces less
if δ < 0, qe (θ, θ) is higher since Pi wants to produce morewhen Pj produces less
) Strategic linkage between Pi�s output and Aj�s cost
![Page 88: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/88.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Bilateral information sharing
Proposition. If both principals share information,
qe (θ, θ) = q�(θ, θ)qe (θ, θj ) < q�(θ, θj ) 8θjqe (θ, θ) > q�(θ, θ) i¤ δ < 0Expected output does not depend on principals�communication decision
The output of type θ is ine¢ ciently low
Because of production externality, this induces Pi to alsodistort the output of type θ when θj = θ:
if δ > 0, qe (θ, θ) is lower since Pi wants to produce lesswhen Pj produces lessif δ < 0, qe (θ, θ) is higher since Pi wants to produce morewhen Pj produces less
) Strategic linkage between Pi�s output and Aj�s cost
![Page 89: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/89.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Bilateral information sharing
Proposition. If both principals share information,
qe (θ, θ) = q�(θ, θ)qe (θ, θj ) < q�(θ, θj ) 8θjqe (θ, θ) > q�(θ, θ) i¤ δ < 0Expected output does not depend on principals�communication decision
The output of type θ is ine¢ ciently low
Because of production externality, this induces Pi to alsodistort the output of type θ when θj = θ:
if δ > 0, qe (θ, θ) is lower since Pi wants to produce lesswhen Pj produces lessif δ < 0, qe (θ, θ) is higher since Pi wants to produce morewhen Pj produces less
) Strategic linkage between Pi�s output and Aj�s cost
![Page 90: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/90.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Unilateral information sharing
Pi shares information, Pj does not
FOCs areEθj
�S1(qei (θ), q
ej (θj , θ))jθ
�= θ
Eθj
�S1(qei (θ), q
ej (θj , θ)jθ
�= θ + ν
1�ν ∆θ
S1(qej (θ, θi ), qei (θi )) = θ 8θi
S1(qej (θ, θi ), qei (θi )) = θ + ν
1�νPr(θi jθ)Pr(θi jθ)
∆θ 8θi
Pi conditions her contracts only on θi , while Pj conditions hercontract on θj and θi
) Pj has a competitive advantage relative to Pi since she canimpose a higher distortion in the less likely states
![Page 91: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/91.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Unilateral information sharing
Pi shares information, Pj does not
FOCs areEθj
�S1(qei (θ), q
ej (θj , θ))jθ
�= θ
Eθj
�S1(qei (θ), q
ej (θj , θ)jθ
�= θ + ν
1�ν ∆θ
S1(qej (θ, θi ), qei (θi )) = θ 8θi
S1(qej (θ, θi ), qei (θi )) = θ + ν
1�νPr(θi jθ)Pr(θi jθ)
∆θ 8θi
Pi conditions her contracts only on θi , while Pj conditions hercontract on θj and θi
) Pj has a competitive advantage relative to Pi since she canimpose a higher distortion in the less likely states
![Page 92: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/92.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Unilateral information sharing
Pi shares information, Pj does not
FOCs areEθj
�S1(qei (θ), q
ej (θj , θ))jθ
�= θ
Eθj
�S1(qei (θ), q
ej (θj , θ)jθ
�= θ + ν
1�ν ∆θ
S1(qej (θ, θi ), qei (θi )) = θ 8θi
S1(qej (θ, θi ), qei (θi )) = θ + ν
1�νPr(θi jθ)Pr(θi jθ)
∆θ 8θi
Pi conditions her contracts only on θi , while Pj conditions hercontract on θj and θi
) Pj has a competitive advantage relative to Pi since she canimpose a higher distortion in the less likely states
![Page 93: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/93.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Unilateral information sharing
Pi shares information, Pj does not
FOCs areEθj
�S1(qei (θ), q
ej (θj , θ))jθ
�= θ
Eθj
�S1(qei (θ), q
ej (θj , θ)jθ
�= θ + ν
1�ν ∆θ
S1(qej (θ, θi ), qei (θi )) = θ 8θi
S1(qej (θ, θi ), qei (θi )) = θ + ν
1�νPr(θi jθ)Pr(θi jθ)
∆θ 8θi
Pi conditions her contracts only on θi , while Pj conditions hercontract on θj and θi
) Pj has a competitive advantage relative to Pi since she canimpose a higher distortion in the less likely states
![Page 94: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/94.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Do principals share information?
Proposition: When agents are privately informedabout their marginal costs:
� If δα < 0, there is a unique equilibrium in dominant strategiesin which both principals share information
� If δα > 0, there is a unique equilibrium in dominant strategiesin which no principal shares information
� If δ = 0, principals are indi¤erent betweensharing information or not
![Page 95: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/95.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Intuition
Principals share information i¤ δα < 0
If δ 6= 0, a correlated distortion e¤ect induces principals tocoordinate outputs:
Suppose that α > 0If Pi shares information, Pj distorts the output of her high-costagent more (i.e. produces less) when θi = θ(since this is less likely than θi = θ)This increases Pi�s pro�ts with strategic substitutes (δ < 0)since Pi wants to produce more when Pj produces lessThis reduces Pi�s pro�ts with strategic complements (δ > 0)since Pi wants to produce less when Pj produces less
The e¤ect is of �rst-order: only the sign of δ mattersand not its magnitude
![Page 96: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/96.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Intuition
Principals share information i¤ δα < 0
If δ 6= 0, a correlated distortion e¤ect induces principals tocoordinate outputs:
Suppose that α > 0If Pi shares information, Pj distorts the output of her high-costagent more (i.e. produces less) when θi = θ(since this is less likely than θi = θ)This increases Pi�s pro�ts with strategic substitutes (δ < 0)since Pi wants to produce more when Pj produces lessThis reduces Pi�s pro�ts with strategic complements (δ > 0)since Pi wants to produce less when Pj produces less
The e¤ect is of �rst-order: only the sign of δ mattersand not its magnitude
![Page 97: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/97.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Intuition
Principals share information i¤ δα < 0
If δ 6= 0, a correlated distortion e¤ect induces principals tocoordinate outputs:
Suppose that α > 0
If Pi shares information, Pj distorts the output of her high-costagent more (i.e. produces less) when θi = θ(since this is less likely than θi = θ)This increases Pi�s pro�ts with strategic substitutes (δ < 0)since Pi wants to produce more when Pj produces lessThis reduces Pi�s pro�ts with strategic complements (δ > 0)since Pi wants to produce less when Pj produces less
The e¤ect is of �rst-order: only the sign of δ mattersand not its magnitude
![Page 98: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/98.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Intuition
Principals share information i¤ δα < 0
If δ 6= 0, a correlated distortion e¤ect induces principals tocoordinate outputs:
Suppose that α > 0If Pi shares information, Pj distorts the output of her high-costagent more (i.e. produces less) when θi = θ(since this is less likely than θi = θ)
This increases Pi�s pro�ts with strategic substitutes (δ < 0)since Pi wants to produce more when Pj produces lessThis reduces Pi�s pro�ts with strategic complements (δ > 0)since Pi wants to produce less when Pj produces less
The e¤ect is of �rst-order: only the sign of δ mattersand not its magnitude
![Page 99: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/99.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Intuition
Principals share information i¤ δα < 0
If δ 6= 0, a correlated distortion e¤ect induces principals tocoordinate outputs:
Suppose that α > 0If Pi shares information, Pj distorts the output of her high-costagent more (i.e. produces less) when θi = θ(since this is less likely than θi = θ)This increases Pi�s pro�ts with strategic substitutes (δ < 0)since Pi wants to produce more when Pj produces less
This reduces Pi�s pro�ts with strategic complements (δ > 0)since Pi wants to produce less when Pj produces less
The e¤ect is of �rst-order: only the sign of δ mattersand not its magnitude
![Page 100: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/100.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Intuition
Principals share information i¤ δα < 0
If δ 6= 0, a correlated distortion e¤ect induces principals tocoordinate outputs:
Suppose that α > 0If Pi shares information, Pj distorts the output of her high-costagent more (i.e. produces less) when θi = θ(since this is less likely than θi = θ)This increases Pi�s pro�ts with strategic substitutes (δ < 0)since Pi wants to produce more when Pj produces lessThis reduces Pi�s pro�ts with strategic complements (δ > 0)since Pi wants to produce less when Pj produces less
The e¤ect is of �rst-order: only the sign of δ mattersand not its magnitude
![Page 101: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/101.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Intuition
Principals share information i¤ δα < 0
If δ 6= 0, a correlated distortion e¤ect induces principals tocoordinate outputs:
Suppose that α > 0If Pi shares information, Pj distorts the output of her high-costagent more (i.e. produces less) when θi = θ(since this is less likely than θi = θ)This increases Pi�s pro�ts with strategic substitutes (δ < 0)since Pi wants to produce more when Pj produces lessThis reduces Pi�s pro�ts with strategic complements (δ > 0)since Pi wants to produce less when Pj produces less
The e¤ect is of �rst-order: only the sign of δ mattersand not its magnitude
![Page 102: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/102.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
The value of communication
Proposition. Principals�expected pro�ts are higher whenthey both share information than with no communication
Since costs are correlated, communication creates aninformational externality that reduces agents�rent
(For small externalities, this e¤ect is stronger thanthe strategic e¤ect due to correlated distortions)
Corollary. Principals�decision not to share information whenδα > 0 does not maximize their joint pro�ts
![Page 103: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/103.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
The value of communication
Proposition. Principals�expected pro�ts are higher whenthey both share information than with no communication
Since costs are correlated, communication creates aninformational externality that reduces agents�rent
(For small externalities, this e¤ect is stronger thanthe strategic e¤ect due to correlated distortions)
Corollary. Principals�decision not to share information whenδα > 0 does not maximize their joint pro�ts
![Page 104: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/104.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
The value of communication
Proposition. Principals�expected pro�ts are higher whenthey both share information than with no communication
Since costs are correlated, communication creates aninformational externality that reduces agents�rent
(For small externalities, this e¤ect is stronger thanthe strategic e¤ect due to correlated distortions)
Corollary. Principals�decision not to share information whenδα > 0 does not maximize their joint pro�ts
![Page 105: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/105.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
The value of communication
Proposition. Principals�expected pro�ts are higher whenthey both share information than with no communication
Since costs are correlated, communication creates aninformational externality that reduces agents�rent
(For small externalities, this e¤ect is stronger thanthe strategic e¤ect due to correlated distortions)
Corollary. Principals�decision not to share information whenδα > 0 does not maximize their joint pro�ts
![Page 106: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/106.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Conclusions
When do principals independently choose to share theinformation obtained from informed agents?
Principals want to:
a¤ect rivals�strategies because of externalitiesreduce agents�information rents
Incentive to share information only depend on the sign of δα
![Page 107: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/107.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Conclusions
When do principals independently choose to share theinformation obtained from informed agents?
Principals want to:
a¤ect rivals�strategies because of externalitiesreduce agents�information rents
Incentive to share information only depend on the sign of δα
![Page 108: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/108.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Conclusions
When do principals independently choose to share theinformation obtained from informed agents?
Principals want to:
a¤ect rivals�strategies because of externalities
reduce agents�information rents
Incentive to share information only depend on the sign of δα
![Page 109: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/109.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Conclusions
When do principals independently choose to share theinformation obtained from informed agents?
Principals want to:
a¤ect rivals�strategies because of externalitiesreduce agents�information rents
Incentive to share information only depend on the sign of δα
![Page 110: Information Sharing between Vertical Hierarchies · ) Interaction between information exchange across organizations and agency con⁄icts within organizations e.g.: Two competing](https://reader033.vdocument.in/reader033/viewer/2022051901/5ff0bb4ad786582c215021e8/html5/thumbnails/110.jpg)
Introduction Model Complete information Asymmetric information Information sharing? Conclusions
Conclusions
When do principals independently choose to share theinformation obtained from informed agents?
Principals want to:
a¤ect rivals�strategies because of externalitiesreduce agents�information rents
Incentive to share information only depend on the sign of δα