# lecture_9 - Game theory What is a game? - Normal-form games...

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ECOS2001 Lecture 9 1 Game theory What is a game? - Normal-form games Dominant strategies – prisoners’ dilemma Nash equilibrium - Pure strategy equilibrium - mixed strategy equilibrium Extensive-form games - two-period games; backwards induction (subgame perfect equilibrium) - entry games; hold-up problem; bargaining

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ECOS2001 Lecture 9 2 Game theory A game has: (1) players; (2) rules; (3) payoffs Used to study situations when interaction is important Often a game can be represented in a payoff matrix Dominant strategy – a player is better off taking a given strategy, regardless as to the strategy of the other player(s).
ECOS2001 Lecture 9 3 Example (3, 3) (1,5 ) (5, 1) (4, 4) Up Down Left Right Harry William

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ECOS2001 Lecture 9 4 Equilibrium outcome - (Up, Left) This is a prisoners’ dilemma, meaning: - each player has a dominant strategy - there is a unique Nash equilibrium - the outcome is not pareto efficient (surplus is not maximised)
ECOS2001 Lecture 9 5 Ways out of a prisoners’ dilemma - surplus is not maximised in prisoners’ dilemma Methods of trying to get out of prisoners’ dilemma 1. govt regulations (restricts choice) 2. repeated game - allows for credible punishment for cheating - reduces the benefit of cheating 3. Credible commitments (pre-game)

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ECOS2001 Lecture 9 6 Nash equilibrium - each player’s strategy is optimal given the strategies of all other players - each player is doing the best they can do given what everybody else is doing - no player has a unilateral incentive to deviate
ECOS2001 Lecture 9 7 Example (2, 4) (1,2) (5, 1) (4, 4) Up Down Left Right Johnno Morgan

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ECOS2001 Lecture 9 8 (3,2) (2,5) (5,2) (4,4) (0,0) (0,0) (0,0) (0,0) (0,0) T M B L CR Player 1 Player 2
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## This note was uploaded on 04/20/2010 for the course ECOS 2001 taught by Professor None during the One '09 term at University of Sydney.

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lecture_9 - Game theory What is a game? - Normal-form games...

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