Maya and Allen Contemplated Going to One of the Two

Essay

Maya and Allen contemplated going to one of the two parties their school buddies organize that night. Just before deciding what party to attend, Allen's cell phone went dead. Now they have to come up with a way to find each other. In their minds, it was as if they play the following game. Each has a choice between two parties, the big one and the small one. The payoffs are as follows: for the strategy combination (big, big)the payoff is (200,200), where the first position refers to Maya, and the second to Allen. Similarly, for (big, small)the payoff is (0, 0), for (small, big)the payoff is (0, 0), while for (small, small)is (500, 500).
a)Does this game have a dominant strategy Nash equilibrium?
b)What are the two pure strategy equilibria?
c)How is this game referred to among game theorists?
d)Is there an equilibrium that is Pareto superior to the other? If yes, is there a possibility Maya and Allen will choose it?