Answer Happy

Q1. Consider the following game: Player 1 X Y Z K (7,5) (5,2) (2,5) (6,1) Player 2 L Best response to X is M. Best response to Z is L. Player 2 does not have a dominant strategy. M (2,2) (3,6) (2,1) (0,0) (4,1) (a) If Player 1 chooses strategy X, what is the best response for Player 2? If, instead, Player 1 chooses strategy Z, what is the best response for Player 2 now? Does Player 2 have a dominant strategy? Justify your answers. (b) What are all the Nash equilibrium outcomes for this game? Which Nash equilibrium outcome is inefficient? Justify your answer. The Nash Equilibrium outcomes are (Y,K) and (Z,L). (Z,L) is an inefficient Nash Equilibrium.

For parts (c) and (d) consider the following game: Player 2 Player 1 A B с (3,3) (x, y) D (y,x) (6,6) (c) If x = -3 and y = 3 in the matrix above, rename each of the strategies A, B, C, and D as "STAG" or "HARE" so that the payoffs are consistent with the stag hunt coordination game we discussed in class. A is renamed as HARE and B is renamed as STAG. C is renamed as HARE and D is renamed as STAG. One possible answer: x=1 and y=8. The dominant strategy for Player 1 is A. The dominant strategy for Player 2 is C. The inefficient Nash Equilibrium is (A,C). (d) Find values for x and y so that the matrix above can be interpreted as a prisoner dilemma. Using your payoffs, identify each player's dominant strategy and the inefficient Nash Equilibrium.