a) Find all Nash equilibria in pure or mixed strategies of the following 2 4 game: 

b) Consider the following game player I chooses a nonnegative real number x, and player II in the same way a nonnegative number y. The resulting (symmetric) payoffs are 

x. (1-y-x) for player 

1, y.(1-x-y) for player II. 

Given x, determine player II's best response y(x) (which is a function of x), and player I's best response x(y) to y. Find a Nash equilibrium, and give the payoffs to the two players. 

c) For the game in (b), find a SPNE of the commitment game, where player I moves first and player II is the follower who moves second. Completely specify the players' strategies, and give the equilibrium payoffs to the two players. 

d) Are the equilibria in (b) and (c) unique? Explain why or why not.

Transcribed Image Text:

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