Question

3. (30 pts) Consider the following game. Players can choose either left () or 'right' (r) The table provided below gives the payoffs to player A and B given any set of choices, where player A's payoff is the firat number and player B's payoff is the second number Player B Player A 4,4 1,6 r 6,1 -3.-3 (a) Solve for the pure strategy Nash equilibria. (4 pta) (b) Suppose player A chooses l with probability p and player B chooses I with probability q Determine player A's best response to any choice of q by player B, and player B's best reaponae to any choice of p by player A. Find the mixed strategy Nash equilibrium. 6 pta) (c) Show these best response functions and all the equilibria on a graph. (6 pta) (d) Now suppose that player B moves first and player A moves second. Show the game information in an extensive form. What is the Naah equilibrium in this case? (8 pts) (e) Would player A prefer the mixed strategy equilibrium in () or the sequential move equilibrium in (d)? Why? (6 pts) 4. (20 pta) Consider the following two-player simultaneoua-move game. Player A chooaea either up'u or down' (d). Player B chooses either left () or ight (r). The table provided below gives the payoffs to player A and B given any set of choices, where player A's payoff is the first number. There are payoffs provided for three versions of this aimple game Game 1 Game 2 Game 3 1. 5 u, 1,1 u,r5,0 10, 10 8,2 d,l 0,5 d,r 4,4 5,1 3,7 2,2 (a) For each of the three games, express the payoff information in the normal form (payoff matrix). (12 pta) (b) For each of the three gamea, determine the pure strategy Nash equilibria. (8 pta)

Answer 1

-3 2 3 ス

9 2 3 BRe 2

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