Exam 3: Focal-Point and Evolutionary Equilibria

-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. The equilibrium strategy profile(s) for this game is(are): I. {First strike, First strike}. II. {Second strike, Second strike}. III. {First strike, Second strike}. IV. {Second strike, First strike}. Which of the following is correct?

-Brad and Angelina are trying to decide how to spend an evening. Brad would prefer tospend an evening at the opera. Angelina would spend the evening attending aprofessional 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 maximin strategy?

The existence of a focal-point equilibrium:

A focal-point equilibrium is possible for:

-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. The strategy profile:

-Consider the Hawk-Dove Game in Figure 3.7. Suppose that the costs (c) and benefits (b)of aggressive behavior $12 and $10, respectively. The evolutionary equilibrium for this game is:

An evolutionary equilibrium:

A Nash equilibrium:

-Consider the noncooperative, static, pricing game depicted in Figure 3.2. Firms A and B can charge a high price or a low price for their products. Payoffs are in thousands of dollars. If larger payoffs are preferred, the Nash equilibrium strategy profile for this game is: I. {High price, High price}. II) {High price, Low price}. III) {Low price, High price}. IV) {Low price, Low price}. Which of the following is correct?

A focal-point equilibrium:

-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. What is the strategy profile for this game if Ben and Jennifer adopt a minimax regret strategy?

-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. What is the strategy profile for this game if Ben and Jennifer adopt a maximin strategy?

-Consider the noncooperative, static, pricing game depicted in Figure 3.2. Firms A and B can charge a high price or a low price for their products. Payoffs are in thousands of dollars. If larger payoffs are preferred, the most likely focal-point equilibrium for this game is: I. {High price, High price}. II. {High price, Low price}. III. {Low price, High price}. IV. {Low price, Low price}. Which of the following is correct?

-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 and hunt 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 Nash equilibrium strategy profile for this game is: I. {Bear, Bear}. II. {Raccoon, Raccoon}. III. {Bear, Raccoon}. IV. {Raccoon, Bear}. Which of the following is correct?

-Consider the Cold War game depicted in Figure 3.6. If both players have a weakly dominant strategy, the equilibrium strategy profile for this game is: I. {First strike, First strike}. II. {Second strike, Second strike}. III. {First strike, Second strike}. IV. {Second strike, First strike}. Which of the following is correct?

A strategy profile that is a focal-point equilibrium:

-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. This game has _____ Nash equilibrium strategy profiles.

-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. If the players in this game are assumed to be rational, the most likely focal-point equilibrium strategy profile for this game is: I. {First strike, First strike}. II. {Second strike, Second strike}. III. {First strike, Second strike}. IV. {Second strike, First strike}. Which of the following is correct?

-Consider the Hawk-Dove Game in Figure 3.7. Suppose that the costs (c) and benefits (b)of aggressive behavior $10 and $12, respectively. The evolutionary equilibrium for this game is:

-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. This game has _____ Nash equilibria.