Lec 14_Game Theory & Oligopoly

7/23/2019 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

Lec 14_Game Theory & Oligopoly

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