Consider the following "dating game," which has two players, A and B, and two strategies, to buy a movie ticket or a baseball ticket. The payoffs, given in points, are as shown in the matrix below. That the highest payoffs occur when both A and B attend the same event.

Assume that players A and B buy their tickets separately and simultaneously. Each must decide what to do knowing the available choices and payoffs but not what the other has actually chosen. Each player believes the other to be rational and self-interested.
a. Does either player have a dominant strategy?
b. How many potential equilibria are there?
c. Is this game a prisoner's dilemma? Explain.
d. Suppose player A gets to buy his or her ticket first. Player B does not observe As choice but knows that A chose first. Player A knows that player B knows he or she chose first. What is the equilibrium outcome?
e. Suppose the situation is similar to part d, except that player B chooses first. What is the equilibrium outcome?

Buy movis cicket Buy ata ay move ticker for B Bay basebal ickss for B 2 for B