Download - Lec 14_Game Theory & Oligopoly
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Game Theory & Oligopoly
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Numerical on competition and
monopoly
P = 100-q
Tc = 40q
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What is game theory
tudy o! rational "eha#ior in situations in$hich your choices a%ect others & theirchoices a%ect you so-called 'games()
*+rame$or, !or thin,ing a"out strategic
interaction
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"out Game Theory
Game theory studies competiti#e and cooperati#e"eha#ior in strategic en#ironments. $here the!ortunes o! se#eral players are intert$ined/
The eld o! game theory "egan around 100
$hen mathematicians "egan as,ing $hetherthere are optimal strategies !or parlor gamessuch as chess and po,er
The rst comprehensi#e !ormulation o! the
su"2ect came in 144 $ith the pu"lication o! the"oo, Theory of Games and Economic Behavior "y!amous mathematician 3ohn #on Neumann andeminent economist Os,ar orgenstern/
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ince then. game theory has "een applied to many otherelds. including political science. military strategy. la$.computer science. and "iology. among other areas/
5n 14 three pioneers in game theory $ere a$arded a
No"el Pri6e. mar,ing the 7arri#al8 o! the eld/
5n 900:. t$o more Game Theorists $ere a$arded theNo"el
Pic, up a "usiness maga6ine or "oo, and there is a goodchance that it $ill use some game theory 2argon; 6ero-sumgame. Prisoner8s
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Terminology andssumptions trategies
ationality
Payo%s >quili"rium
?ommon ,no$ledge
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ssumptions
ationality ?omplete ,no$ledge o! one8s interests
+la$less calculation o! $hat actions "est
ser#e those interests
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?ommon @no$ledge ?ommon understanding o! the ,ey
elements o! the game
Aist o! players
trategies
Payo%s
ssumption that each player is a rationalmaBimi6er
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The imultaneous Game
The strategic en#ironment Who are theplayersC
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naly6ing Games; N?1///
2 X 2; Player 1 plays Up or Do$nDPlayer 9 plays Le!t or Right/ Payo%s;E.A)=4.1). E.)=F.9).
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Game N?1
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naly6ing Games; N?9
2 X 2; Player 1 plays Up or Do$nDPlayer 9 plays Le!t or Right/ Payo%s;E.A)=4.9). E.)=F.1).
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Nash >quili"rium
E.A) is a Nash >quili"rium o! the game i! and only iPE. A) I P
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Nash >quili"rium
Player 1 thin,s ; can 5 do "etter "y unilateral de#iationCPlayer 9 thin,s ; can 5 do "etter "y unilateral de#iationC
5! ans$er to "oth questions is 7no8 then E. A) is a Nash
>quili"rium
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?ournot quili"rium is a choice o! q1.q9 s/trm 1 maBimi6es 1 gi#en q9 andrm 9 maBimi6es 9 gi#en q1
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>quili"rium
1 = 100-q1-q9)q1 J 40q1
d1Kdq1 = L0-9q1-q9 =0 1)
9 = 100-q1-q9)q9 J 40q9
d9Kdq9 = L0-9q9-q1 =0 9)
ol#ing 1) and 9)
H1M =q9M = 90
PM = L0
1M=9M = 400
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est response cur#es
ol#ing 1) and 9)H1M =q9M = 90PM = L0
1M=9M = 400
q9
q1
F0
F090
90
+irm 1est response
+irm 9est response
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5mpact o! cost reduction
uppose +irm 1 reduces total cost toF0q1q9
q1
F0
F090
90
+irm 1 N>West response
+irm 9est response
F:
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Aet8s play
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Please !orm L groups $ith a"out mem"ers each
elect one 7communicator8 $ho $ill "e
responsi"le !or communicating groupdecisions on ho$ to play
>ach group $ill play the !ollo$ing gameagainst one other group Q times
The identity o! the corresponding group isnot ,no$n "ut the same group $ill staythe same
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ules o! the Game
>ach group has a red card and a"lac, card/
?hoose one o! the t$o cards $ithout,no$ing $hat others ha#e chosen)/
5! you ha#e chosen a red card 5 $illgi#e you 10 rupees/
5! you ha#e chosen a "lac, card 5 $illgi#e your partner F0 rupees
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t the end o! each round the payo%s$ill "e communicated to each group
The group $ill get a couple o!minutes !or consultation and thenha#e to play again
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The 5ncenti#e
The mem"ers o! the "est group $illget a ,it ,at each
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?artel
oth decide to produce a lo$eroutput to achie#e monopoly protand di#ide the prot equally
oth agree that they $ill produce 1:units each
uppose one rm "rea,s the
agreementC
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?artel
Firm 1:450,
Firm 2: 450
F1: 375
F2: 500
F1:500,
F2: 375
F1: 400
F2: 400
1:
90
1: 90
+irm 1
+irm 9
oth rms $ill produce 90