Evangeline and Gabriel met at a freshman mixer. They want desperately to meet each other again, but they forgot to exchange names or phone numbers when they met the first time. There are two possible strategies available for each of them. These are Go to the Big Party or Stay Home and Study. They will surely meet if they both go to the party, and they will surely not otherwise. The payoff to meeting is 1,000 for each of them. The payoff to not meeting is zero for both of them. The payoffs are described by the matrix below.
(a) A strategy is said to be a weakly dominant strategy for a player if the payoff from using this strategy is at least as high as the payoff from using any other strategy. Is there any outcome in this game where both players are using weakly dominant strategies? ________.
(b) Find all of the pure-strategy Nash equilibria for this game. ________.
(c) Do any of the pure Nash equilibria that you found seem more reasonable than others? Why or why not? ________.
(d) Let us change the game a little bit. Evangeline and Gabriel are still desperate to find each other. But now there are two parties that they can go to. There is a little party at which they would be sure to meet if they both went there and a huge party at which they might never see each other. The expected payoff to each of them is 1,000 if they both go to the little party. Since there is only a 50-50 chance that they would find each other at the huge party, the expected payoff to each of them is only 500. If they go to different parties, the payoff to both of them is zero. The payoff matrix for this game is:
(e) Does this game have a dominant strategy equilibrium? No. What are the two Nash equilibria in pure strategies? ________.
(f) One of the Nash equilibria is Pareto superior to the other. Suppose that each person thought that there was some slight chance that the other would go to the little party. Would that be enough to convince them both to attend the little party? No. Can you think of any reason why the Pareto superior equilibrium might emerge if both players understand the game matrix, if both know that the other understands it, and each knows that the other knows that he or she understands the game matrix? ________.