class 19 cournot_post

class 19 cournot_post - Class 19 Nash Equilibrium and Nash...

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Class 19 ash Equilibrium and Nash Equilibrium and Cournot
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Problem Set ote the Reading ± Note the Reading ± Do the problem set before the next lecture: You train today’s material and prepare for next time
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Last Time undamentals: p H p M p L p H 5 / 5 2 / 8 1 / 7 Fundamentals: Actions: A i = { a 1 , a 2 , ….} references: a “ ayoffs” p M 8 / 2 4 / 4 1.5 / 6 p L 7 / 1 6 / 1.5 2 / 2 Preferences: u i (a i , a -i ) Payoffs Strictly Dominated Actions (Strategies): n action strictly dominated for An action a i is strictly dominated for player i if there is some action a’ i such that a < a r all u i (a i , a -i ) < u i (a i , a -i ) for all a -i Strictly dominant strategy Playing action a is a strictly dominant strategy, if for all a’ i u i (a i , a -i ) > u i (a’ i , a -i ) for all a -i
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Last Time undamentals: Fundamentals: Actions: A i = { a 1 , a 2 , ….} references: a “ ayoffs” p H p L p H $5M / $5M $1M / $7M Preferences: u i (a i , a -i ) Payoffs Strictly Dominated Actions (Strategies): n action strictly dominated for p L $7M / $1M $2M / $2M An action a i is strictly dominated for player i if there is some action a’ i such that a < a r all Prisoners’ Dilemma: What is the problem of setting high prices? Why can’t they cooperate? u i (a i , a -i ) < u i (a i , a -i ) for all a -i Strictly dominant strategy Idea: Game describes everything. Playing action a is a strictly dominant strategy, if for all a’ i u i (a i , a -i ) > u i (a’ i , a -i ) for all a -i If they can write contracts, punish each other in the future, etc, we have to include this in the game.
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Outline ash Equilibrium ± Nash Equilibrium ± A Model of an Oligopoly: Cournot
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Nash Equilibrium Nash Equilibrium Hawk Dove Hawk -1 / -1 5 / 1 An action profile ( a* 1 , a* 2 ) is a Nash Equilibrium if: * a* a* f r all Hawk-Dove (Chicken) Dove 0 / 5 2.5 / 2.5 u 1 (a 1 ,a 2 ) u 1 (a 1 2 ) oa a 1 u 2 (a* 1 , a* 2 ) u 2 (a* 1 , a’ 2 ) for all a’ 2 () The players can split $5 and behave “hawkish” or “dovish”.
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This note was uploaded on 12/10/2011 for the course ECON 401 taught by Professor Burbidge,john during the Winter '08 term at Waterloo.

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class 19 cournot_post - Class 19 Nash Equilibrium and Nash...

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