week5-class-print - In this lecture Nash Equilibrium 1....

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ECOS3012 - Strategic Behavior School of Economics, FASS University of Sydney Lecture 5, March 30, 2011 ECOS3012 - Strategic Behavior (USYD) Nash Equilibrium Lecture 5, March 30, 2011 1 / 14 In this lecture 1. Nash Equilibrium. 2. and Nash Equilibrium and IEDS. 3. Characterization of Nash equilibria I Using calculus methods. I Using properties of mixed strategies. ECOS3012 - Strategic Behavior (USYD) Nash Equilibrium Lecture 5, March 30, 2011 2 / 14 Nash Equilibrium Definition 1 A strategy profile ( s * 1 , . . . , s * n ) is said to be a Nash equilibrium of a given strategic form game if player i , s * i is a best response to s * - i . I This is by far the most important solution concept in game theory. I In at a Nash equilibrium, no player has a unilateral incentive to choose a different strategy. I Since every player’s choice is a best response to the other, it is simply the point where the reaction functions of the different players intersect. ECOS3012 - Strategic Behavior (USYD) Nash Equilibrium Lecture 5, March 30, 2011 3 / 14 Nash Equilibrium Recall that in a Nash equilibrium, each player maximizes his/her payoff given the strategies of the other players. Two questions Q1 A Nash equilibrium is only immune to unilateral deviations , but players may benefit by forming a joint deviations by a coalition . Typical answer: If it is possible for coalitions to form, then one ought to include that as part of the strategy description and study that (meta)game. Q2 How do players coordinate on equilibrium play? What is the justification for Nash equilibrium as a prediction of human behavior? Typical Answer 1: (Eductive justification) Suppose that we are able to come up with a theory of of a game should be played. If this theory is common-knowledge, it better be the case that it is immune to unilateral deviations – otherwise the theory itself is undermined. Typical Answer 2: (Evolutionary and/or learning justification) Players play “similar” games over a long period of time. Suppose play were to eventually reach a “steady state”. Then by definition, the outcome will be immune to unilateral deviations. ECOS3012 - Strategic Behavior (USYD)
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This note was uploaded on 08/20/2011 for the course ECON 101 taught by Professor Etw during the Spring '11 term at Università di Bologna.

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week5-class-print - In this lecture Nash Equilibrium 1....

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