Consider the following game, expressed in dollar terms: L R U $3,$2 $0.$1 D $1,50 $2,$1 (a) Suppose, first, that this game is played by two egoists, for whom u(x,y)=x. Compute all Nash equilibria in pure strategies. (5 points) (b) Is there an equilibrium in mixed strategies? If there is, compute the probability p with which player I plays U and the probability q with which player Il plays L. Also, compute the amount of utility each player gets in the equilibrium. (5 points) (c) Are any of these Nash equilibria trembling-hand perfect? (5 points) (d) Suppose, next, that this game is played by two utilitarians, for whom u(x,y)=x+y. Compute all Nash equilibria in pure and mixed strategies. (5 points)

Consider the following game, expressed in dollar terms: L R U $3,$2 $0.$1 D $1,50 $2,$1 (a) Suppose, first, that this game is played by two egoists, for whom u(x,y)=x. Compute all Nash equilibria in pure strategies. (5 points) (b) Is there an equilibrium in mixed strategies? If there is, compute the probability p with which player I plays U and the probability q with which player Il plays L. Also, compute the amount of utility each player gets in the equilibrium. (5 points) (c) Are any of these Nash equilibria trembling-hand perfect? (5 points) (d) Suppose, next, that this game is played by two utilitarians, for whom u(x,y)=x+y. Compute all Nash equilibria in pure and mixed strategies. (5 points)

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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