rules and commitment in communicationequilibriumpredictions generalframework sender receiver...
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Rules and Commitment in Communication
Guillaume Frechette Alessandro Lizzeri Jacopo Perego
September 2018
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Overview introduction
We study strategic information transmission with (partial)commitment.
Recently, a lot of interest in the implications of commitment incommunication:
▶ Design incentives via information Kamenica and Gentzkow (2011)Bergemann and Morris (2016, 2018)Mathevet, Perego, and Taneva (2017)
▶ Political campaigns Alonso and Camara (2016)Chan, Gupta, Li and Wang. (2017)
▶ Rating systems Duffie, Dworczak, and Zhu (2017)
▶ Stress tests for the banking system Inostroza and Pavan (2017)
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Overview introduction
Despite all this attention, the baseline model mostly lacksempirical corroboration:
▶ Information can be notoriously hard to “measure” in the field.
▶ Identifying variations in commitment can also be quiteproblematic.
This paper:
Introduce a novel framework that allows for a comprehensiveexperimental assessment of the role of commitment incommunication.
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What is Commitment introduction
State isrealized
Sender SelectsStrategy
Message isTransmitted
Receiverplays
No Commitment
Sender choosesa strategy
State isrealized
Message istransmitted
Receiverplays
Full Commitment
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What is Commitment introduction
State isrealized
Sender SelectsStrategy
Message isTransmitted
Receiverplays
No Commitment
Sender choosesa strategy
State isrealized
Message istransmitted
Receiverplays
Full Commitment
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Special Cases introduction
▶ Cheap Talk. Crawford and Sobel (1982)
− No commitment and unverifiable information.
▶ Disclosure. Grossman (1981), Milgrom (1981), Okuno-Fujiwara et al (1990)
− No commitment and verifiable Information.
▶ Bayesian Persuasion. Kamenica and Gentzkow (2011)
− Full commitment and Unverifiable information.
Variations around a common basic structure, different predictions.
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Literature in Lab and Field introduction
▶ Cheap talk experiments: Dickhaut, McCabe, and Mukherji(1995); Blume, De Jong, Kim, and Sprinkle (1998); Cai and Wang(2006); Sanchez-Pages and Vorsatz (2007); Wang, Spezio,Camerer (2010)
▶ Disclosure experiments: Forsythe, Isaac, and Palfrey (1989);King and Wallin (1991); Dickhaut, Ledyard, Mukherji, and Sapra(2003); Forsythe, Lundholm, and Rietz (1999); Benndorf, K?bler,and Normann (2015); Hagenbach and Perez-Richet (2015); Jin,Luca, and Martin (2016)
▶ Disclosure field: Mathios (2000); Jin and Leslie (2003); Dranoveand Jin (2010)
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What We Do introduction
We introduce a theoretical framework nesting the existing modelsof communication under the same umbrella.
▶ This framework generates comparative statics that we use toexplicitly test the role of commitment in communication.
▶ Moreover, it gives us a broader perspective on thecommunication literature.
1. A critical assessment of over-communication in cheaptalk.
2. A novel policy role for rules governing communication.
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Main Results introduction
▶ Data match qualitative predictions of the model providingvalidation of the strategic rational behind the role ofcommitment commitment in communication.
▶ There are also interesting quantitative deviations.
▶ Most notably, we find that rules matter, in ways that areentirely unpredicted by the theory. (policy implications)
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benchmark treatment
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Setting the Stage benchmark treatment
We start with a simple implementation of a persuasion game.
▶ Goal is to characterize a number of basic facts about sendersand receivers’ behavior.
Moreover, this benchmark treatment allows us to
▶ Introduce main ingredients of the design▶ Familiarize with the main strategic tensions
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The Base Game benchmark treatment
A Sender-Receiver binary guessing game.
▶ Binary payoff-state θ ∈ {B,R}, prior belief µ0(R) = 13 .
▶ Sender sends messages (b or r) to Receiver as a function ofthe state.
▶ Preferences are misaligned:
− Receiver’s payoff is 1 if she guesses the state correctly.
− Sender’s payoff is 1 if Receiver guesses red.
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Implementation benchmark treatment
Sender communicates under commitment.
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Implementation benchmark treatment
Receiver responds by guessing the state.
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Main Strategic Tension benchmark treatment
▶ Sender wants to persuade Receiver to guess red.
▶ Absent communication, Receiver should always guess blue.
▶ With communication, the equilibrium predicts thatmessager b
State R 100% 0B 50% 50%
▶ Sender exploits commitment to strategically lie when state isB, but just enough to maintain credibility.
▶ Commitment assumption is key.
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Main Strategic Tension benchmark treatment
▶ Sender wants to persuade Receiver to guess red.
▶ Absent communication, Receiver should always guess blue.
▶ With communication, the equilibrium predicts thatmessager b
State R 100% 0B 50% 50%
▶ Sender exploits commitment to strategically lie when state isB, but just enough to maintain credibility.
▶ Commitment assumption is key.
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Potential Challenges benchmark treatment
Simple in theory. In practice, it is more subtle.
▶ Sender’s task is non-trivial: she needs to optimally design aninformation policy.
▶ Bayesian paradigm: Receiver needs to be Bayesian, Senderneeds to be Bayesian and believe Receiver is Bayesian, etc.
▶ Understanding commitment power: how to use it, how toreact to it.
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preliminary results
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Results: Senders benchmark treatment
Fact 1.Senders induce posteriors that on average are in line withtheoretical predictions.Moreover, they communicate by employing a natural language.
02
46
810
0 .2 .4 .6 .8 1Posterior on Red
RedBlue
Dashed lines indicate median posterior.
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Results: Senders benchmark treatment
Fact 2. Most senders do engage in communication strategies thatare somewhat sophisticated.
We use k-means clustering algorithm to create behavioral types.
This categorization is quite clean: 88% of data fall in threemeaningful types:
▶ Under-communication – 24%▶ Equilibrium-like – 35%▶ Over-communication – 29%
Fact 3. Do so persistently.
Median sender plays a strategy in the same cluster nine times outof ten.
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Results: Senders benchmark treatment
Fact 2. Most senders do engage in communication strategies thatare somewhat sophisticated.
We use k-means clustering algorithm to create behavioral types.
This categorization is quite clean: 88% of data fall in threemeaningful types:
▶ Under-communication – 24%▶ Equilibrium-like – 35%▶ Over-communication – 29%
Fact 3. Do so persistently.
Median sender plays a strategy in the same cluster nine times outof ten.
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Results: Senders benchmark treatment
Fact 2. Most senders do engage in communication strategies thatare somewhat sophisticated.
We use k-means clustering algorithm to create behavioral types.
This categorization is quite clean: 88% of data fall in threemeaningful types:
▶ Under-communication – 24%▶ Equilibrium-like – 35%▶ Over-communication – 29%
Fact 3. Do so persistently.
Median sender plays a strategy in the same cluster nine times outof ten.
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Results: Senders benchmark treatment
Figure 1: Sender’s Strategy Grouped in Clusters
0 25 50 75 100
Probability of Message r Conditional on State R
0
25
50
75
100
Pro
bab
ilit
yof
Mes
sageb
Con
dit
ion
alon
Sta
teB
Large symbols indicate center of the cluster
High Informativeness: 29% of plays
Partial Informativeness: 35% of plays
Low Informativeness: 24% of plays
Residual Cluster: 13% of plays
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Results: Receivers benchmark treatment
Fact 4.Receivers’ behavior:
▶ Bayesian paradigm does a poor job at predicting receiversbehavior.
▶ Yet, they do react to information, and their behavior can beexplained by threshold strategies.
▶ Large heterogeneity: they differ in the amount of informationthey require to be successfully persuaded.
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Results: Receivers benchmark treatment
0.0
0.2
0.4
0.6
0.8
1.0
BlueTh
resh
olds
0.0 0.2 0.4 0.6 0.8 1.0 BlueBayesian Responder Threshold
Diamonds for subjects harder to convince than a Bayesian, square for subjects easier to convince than a Bayesian, circle otherwise.Hollow marker for subjects whose threshold is accurate in less than 80% of cases.Blue indicates a subject who's choices are best explained by the rule always guess blue.Values are jittered slightly to make multiple overlapping thresholds distinguishable.
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Results: Takeaways benchmark treatment
Two qualitative takeaways:
1. Despite all these deviations, what about the main qualitativeprediction of the model, strategic lying?
0.0 0.2 0.4 0.6 0.8 1.0
Probability of Blue Message when State is Blue
0.0
0.2
0.4
0.6
0.8
1.0
Estimated Expected Payoff for Sender
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Results: Takeaways benchmark treatment
Two qualitative takeaways:
1. Despite all these deviations, what about the main qualitativeprediction of the model, strategic lying?
0.0 0.2 0.4 0.6 0.8 1.0
Probability of Blue Message when State is Blue
0.0
0.2
0.4
0.6
0.8
1.0
Estimated Expected Payoff for Sender
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Results: Takeaways benchmark treatment
Two qualitative takeaways:
2. A critical assessment of existing experimental evidence oncommunication.
A central finding in the literature on experimental cheap talkis over-communication.
“Players tend to be truthful as a sender and credulous as areceiver.” (Blume et al., 2017)
Some of our findings contrast this conclusion.− Increasing commitment.
− Behavior in revision stage.
− Analysis in U100S: communication types.
− Comparative statics U vs V.
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Results: Takeaways benchmark treatment
Two qualitative takeaways:
2. A critical assessment of existing experimental evidence oncommunication.
A central finding in the literature on experimental cheap talkis over-communication.
“Players tend to be truthful as a sender and credulous as areceiver.” (Blume et al., 2017)
Some of our findings contrast this conclusion.− Increasing commitment.
− Behavior in revision stage.
− Analysis in U100S: communication types.
− Comparative statics U vs V.
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general framework
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Commitment in Communication general framework
Two main limitations in the previous analysis
▶ It does not quite address the defining assumption inpersuasion: the role commitment.
▶ We did not provide an actual “test” for how commitmentaffects subjects behavior.
Simply, we cannot address these more substantive questions inthe context our benchmark model.
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A Richer Model general framework
To do so, we need to enrich our model and we do so in twodirections:
1. Allow for partial commitment.
2. Introduce verifiable information (what we call “rules”)
The value of this richer model is twofold.
▶ The interaction between commitment and rules generatessharp comparative statics that we use to test persuasion.
▶ Umbrella framework. A broader perspective oncommunication games.
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A Richer Model general framework
To do so, we need to enrich our model and we do so in twodirections:
1. Allow for partial commitment.
2. Introduce verifiable information (what we call “rules”)
The value of this richer model is twofold.
▶ The interaction between commitment and rules generatessharp comparative statics that we use to test persuasion.
▶ Umbrella framework. A broader perspective oncommunication games.
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1. What is Partial Commitment? general framework
1. Commitment Stage
− Sender chooses an informationstructure.
2. Revision Stage
− Sender learns the state.− She can revise her message.
with prob ρ with prob 1− ρ
message
3. Guessing Stage
− Receiver observes message and guesses thestate.
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1. What is Partial Commitment? general framework
1. Commitment Stage
− Sender chooses an informationstructure.
2. Revision Stage
− Sender learns the state.− She can revise her message.
with prob ρ with prob 1− ρ
message
3. Guessing Stage
− Receiver observes message and guesses thestate.
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1. What is Partial Commitment? general framework
1. Commitment Stage
− Sender chooses an informationstructure.
2. Revision Stage
− Sender learns the state.− She can revise her message.
with prob ρ with prob 1− ρ
message
3. Guessing Stage
− Receiver observes message and guesses thestate.
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1. What is Partial Commitment? general framework
1. Commitment Stage
− Sender chooses an informationstructure.
2. Revision Stage
− Sender learns the state.− She can revise her message.
with prob ρ with prob 1− ρ
message
3. Guessing Stage
− Receiver observes message and guesses thestate.
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2. What are Rules? general framework
Enrich the message space: r, b and n.
Then, we consider two extreme situations:
− Unverifiable information. As in cheap talk models
Sender can send whichever message she wants.
− Verifiable information. As in models of disclosure
If state is R, Sender can’t send message b message.If state is B, Sender can’t send message r message.
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Interacting Rules and Commitment general framework
TheoremUnder unverifiable information, increasing commitmentincreases informativeness.
Under verifiable information, increasing commitment decreasesinformativeness.
Remark
At ρ = 1 (full commitment), equilibrium informativeness isrule-independent.
Therefore, rules are predicted to have no welfare effect under fullcommitment.
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Interacting Rules and Commitment general framework
TheoremUnder unverifiable information, increasing commitmentincreases informativeness.
Under verifiable information, increasing commitment decreasesinformativeness.
Remark
At ρ = 1 (full commitment), equilibrium informativeness isrule-independent.
Therefore, rules are predicted to have no welfare effect under fullcommitment.
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Interacting Rules and Commitment general framework
0 1
Degree ofCommitment
FullyInformative
OptimalLevel
NoInformation
Verifiable
Unverifiable
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Main Strategic Tension (Revisited) general framework
Sender’s equilibrium behavior in two extreme cases:
U100messages
r b n
State R 100% 0 0B 50% 50% 0
V100messages
r b n
State R 0 0 100%B 0 50% 50%
Intuition:
− U100. Lie as much as you can, but preserve incentives.− V100. Conceal the good news: “No news, good news.”
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Treatments general framework
Our Treatments (2x3 factorial design):
Rules: Verifiable (V) vs Unverifiable (U).Commitment: ρ ∈ {20, 80, 100}.
Commitment
Rules V20 V80 V100U20 U80 U100
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Treatments general framework
0 1
Degree ofCommitment
FullyInformative
OptimalLevel
NoInformation
Verifiable
Unverifiable
U20
U80
V20
V80UV100
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Equilibrium Predictions general framework
Sender ReceiverCommitment Revision Guessing
Treat. Ball Message Ball Message Mes. Guess
red blue no red blue no
R 1 0 R 1 0 red redV20 B x 1 − x B x 1 − x blue blue
no blueR 0 1 R 1 0 red red
V80 B 34
14 B 0 1 blue blue
no red
R 0 1 red redV100 B 1
212 blue blue
no red
R x y 1 − x − y R 1 0 0 red blueU20 B x y 1 − x − y B 1 0 0 blue blue
no blueR 1 0 0 R 1 0 0 red red
U80 B 38
58 0 B 1 0 0 blue blue
no blueR 1 0 0 red red
U100 B 12
12 0 blue blue
no blue
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Experimental Details general framework
Implementation:
− Two unpaid practice rounds.− 25 periods in fixed roles (last 10 for data analysis).− Random rematching between periods.
General Information:
− Six treatments, four sessions per treatment.− 384 subjects (≈ 16 per session; between 12 and 24).− Average earnings: $24 (including $10 show up fee).− Average duration: 100 minutes.
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main results
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Testing Commitment: Senders main results
Do Senders understand and use commitment power?
Identification Strategy:
▶ Focus on treatments of partial commitment
▶ Compare Senders’ behavior between Commitment Stage andRevision Stage.
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Testing Commitment: Senders main results
Figure 2: Sender’s Strategy: Commitment vs. Revision, ρ = 0.8
If Ball is Red If Ball is Blue
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Informativeness in U80:
Commitment stage: 0.43
Revision stage: 0.02
Treatment U80
Change for Red Message
Change for Blue Message
Change for None Message
If Ball is Red If Ball is Blue
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Informativeness in V80:
Commitment stage: 0.83
Revision stage: 0.99
Treatment V80
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Testing Commitment: Senders main results
We draw two main conclusions:
▶ Senders do react to commitment.
▶ Moreover, as predicted by the theory, the change in behaviorbetween commitment and revision stage are in oppositedirections with verifiable vs. unverifiable messages.
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Testing Commitment: Receivers main results
Do Receivers understand the implications of Senders’ commitmentpower?
Identification Strategy:
▶ Isolate messages with the same “Commitment-Stage”informational content.
▶ Compare Receivers’ guesses in U20 vs U100 (V20 vs V100)conditional on those messages.
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Testing Commitment: Sender main results
Figure 3: Receiver’s Response to Persuasive Messages: ρ = 0.2 vs. ρ = 1
0.0 0.2 0.4 0.6 0.8 1.0Induced Posterior Belief from Commitment Stage given Message Red
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Treatment U20Treatment U100
0.0 0.2 0.4 0.6 0.8 1.0Induced Posterior Belief from Commitment Stage given Message Empty
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Treatment V20Treatment V100
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Testing Commitment: Receivers main results
We draw two main conclusions:
▶ Receivers do react to commitment power.
▶ Moreover, they do so in ways predicted by the theory.
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Main Comparative Statics main results
Next, we test our main comparative statics.
Recall our main result:
▶ Under unverifiable information, increasing commitmentincreases informativeness.
▶ Under verifiable information, increasing commitmentdecreases informativeness.
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Main Comparative Statics main results
0.00 0.25 0.50 0.75 1.00
Bayesian Correlations (By Sender)
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centi
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U100
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Bayesian Correlations (By Sender)
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V100
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Main Comparative Statics main results
0.00 0.25 0.50 0.75 1.00
Bayesian Correlations (By Sender)
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Main Comparative Statics main results
We observe a first-order stochastic
▶ increase in the distribution of informativeness wheninformation is unverifiable.
▶ decrease in the distribution of informativeness wheninformation is verifiable.
Overall, the model does a pretty good job at matching thesequalitative predictions.
Increasing commitment:
Unverifiable: Truthfully revealing bad news.Verifiable: Strategically concealing good news.
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The Role of Rules main results
So far rules are purely instrumental.
A concluding aside on rules in communication.
Remark
At ρ = 1 (full commitment), equilibrium informativeness isrule-independent.
Therefore, rules are predicted to have no welfare effect under fullcommitment.
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The Role of Rules main results
And yet... Rules matter disproportionately (when they shouldn’t):
0.00 0.25 0.50 0.75 1.00Bayesian Correlations (By Sender)
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Role of Rules main results
Why?
U100messages
r b n
Ball R 100% 0 0B 50% 50% 0
V100messages
r b n
Ball R 0 0 100%B 0 50% 50%
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The Role of Rules
Figure 4: Sender’s Strategy Grouped in Clusters
0 25 50 75 100
Probability of Red Message Conditional on Red Ball
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25% of plays
32% of plays
28% of plays
16% of plays
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The Role of Rules main results
In the data, we observe a combination of:
▶ Senders’ failure to fully embrace a strategy in which goodnews are concealed.
▶ Receivers’ are overly (i.e. more than Bayesian) skeptical aboutsilence.
The art of concealing information is not a simple one.
An increased policy role for the introduction of rules.
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A broader perspective
▶ A key finding in the literature on experimental cheap talk isover-communication.
▶ “Players tend to be truthful as a sender and credulous as areceiver.” (Blume et al., 2017)
▶ Some of our findings contrast this conclusion.
− Increasing commitment.
− Behavior in revision stage.
− Analysis in U100S: communication types.
− Comparative statics U vs V.
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conclusion
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Conclusion
▶ The first experimental assessment of Bayesian Persuasion.
▶ We designed tests via a novel framework that nests existingcommunication models under the same umbrella.
▶ Subjects react to commitment and match the qualitativepredictions of our model.
▶ Substantial heterogeneity and existence of persistentcommunication types.
▶ An over-reaction to rules and its policy-implications.
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Correlations by Treatment
Theory:Commitment (ρ)
20% 80% 100%
Verifiable 1 0.57 0.50
Unverifiable 0 0.50 0.50
Data:Commitment (ρ)
20% 80% 100%
Verifiable 0.80 ≈ 0.78 > 0.67∨ ∨
Unverifiable 0.09 < 0.21 ≈ 0.21
Data + Bayesian Rec:Commitment (ρ)
20% 80% 100%
Verifiable 0.89 ≈ 0.85 > 0.78∨ ∨
Unverifiable 0.00 < 0.33 ≈ 0.34
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Correlations by Treatment
Theory:Commitment (ρ)
20% 80% 100%
Verifiable 1 0.57 0.50
Unverifiable 0 0.50 0.50
Data:Commitment (ρ)
20% 80% 100%
Verifiable 0.80 ≈ 0.78 > 0.67∨ ∨
Unverifiable 0.09 < 0.21 ≈ 0.21
Data + Bayesian Rec:Commitment (ρ)
20% 80% 100%
Verifiable 0.89 ≈ 0.85 > 0.78∨ ∨
Unverifiable 0.00 < 0.33 ≈ 0.34
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Estimated Thresholds and Precisions
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Blue indicates a subject who's choices are best explained by the rule always guess blue.Values are jittered slightly to make multiple overlapping thresholds distinguishable.
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Thresholds: Receivers vs Bayesian
0.00.20.40.60.81.0
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V20
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V100
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U20
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U80
0.00.20.40.60.81.0
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U100
Black for subjects harder to convince than a Bayesian, gray for subjects easier to convince than a Bayesian.Blue indicates a subject who's choices are best explained by the rule always guess blue.Values are jittered slightly to make multiple overlapping thresholds distinguishable.Only includes responders for whom the best fitting threshold accounts for at least 80% of choices.
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Enlarging Message Space
0.0 0.2 0.4 0.6 0.8 1.0Bayesian Correlation (by sender)
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