Exam 3: Focal-Point and Evolutionary Equilibria

-Consider the pie-sharing game depicted in Figure 3.3. Greta has baked an apple pie for her two sons Hans and Frans. Hans and Frans simultaneously ask for a slice of the pie. Greta tells her sons that they can have any size slice they want as long as their slices do not exceed the entire pie. On the other hand, if their combined requests exceed the size of the pie then they each get nothing. The most likely focal-point equilibrium for this game is:

The qualitative factors that help to explain the existence of a focal-point equilibrium include:

-Consider the Cold War game depicted in Figure 3.6 involving a first and second strike nuclear strategies where !4 represents total annihilation, !L represents significant but "acceptable" losses, and G_US and G_SU represent positive gains to the U.S. and the Soviet Union, respectively. Both players have:

-Brad and Angelina are trying to decide how to spend an evening. Brad would prefer to spend an evening at the opera. Angelina would spend the evening attending a professional wrestling match. They could, of course, go their separate ways, but would rather spend the evening together. Figure 3.4 summarizes the payoffs from alternative strategy profiles. The most likely focal-point equilibrium strategy profile for this game is:

-Brad and Angelina are trying to decide how to spend an evening. Brad would prefer to spend an evening at the opera. Angelina would spend the evening attending a professional wrestling match. They could, of course, go their separate ways, but would rather spend the evening together. Figure 3.4 summarizes the payoffs from alternative strategy profiles. What is the strategy profile for this game if Brad and Angelina adopt a minimax regret strategy?

-Consider the noncooperative, static game depicted in Figure 3.1. Two hunters are stalking bear or raccoon. Each could hunt raccoon alone, or they can coordinate their efforts by hunting bear. Sharing a bear is preferred to sharing a raccoon. The payoffs in this game are measured in units of satisfaction. If larger payoffs are preferred, the most likely focal-point equilibrium for this game is: I. {Bear, Bear}. II. {Raccoon, Raccoon}. III. {Bear, Raccoon}. IV. {Raccoon, Bear}. Which of the following is correct?

Framing:

-Ben and Jennifer are trying to decide how to spend an evening. Ben would like to attend a ballet performance. Jennifer would like to go to a hockey game. While they could spend the evening apart, they would prefer to spend the evening together. Figure 3.5 summarizes the payoffs from alternative choices. The most likely focal-point equilibrium strategy profile for this game is:

Coordination games:

In games involving multiple Nash equilibria, several qualitative factors appear to be important in explaining the existence of a focal-point equilibrium, including: I. Distribution of payoffs. II. Equity. III. Diversity. IV. Fairness. V. Uniqueness. Which of the following is correct?

When attempting to identify a unique focal-point equilibrium in static games:

-Brad and Angelina are trying to decide how to spend an evening. Brad would prefer to spend an evening at the opera. Angelina would spend the evening attending a professional wrestling match. They could, of course, go their separate ways, but would rather spend the evening together. Figure 3.4 summarizes the payoffs from alternative strategy profiles. This game has _____ Nash equilibrium strategy profiles.