Exam 12: Game Theory

Use the following to answer question: Figure 12.11 -(Figure 12.11)

The game has two players, each with three strategies. a. Identify and list any dominant strategies. b. Using the check method, find all pure Nash equilibria in the game.

Which of the following games is solvable by backward induction?

The table contains letters that represent payoff values. If the strategy combination (B , Y) is a Nash equilibrium, then prove that the strategy combination (A , X) must also be a Nash equilibrium assuming there are no dominant strategies. Assume that no two letters will take on the same value.

Use the following to answer questions 47-48: Figure 12.10 -(Figure 12.10) In the figure, payoffs are profits in millions of dollars. Suppose that Feely cannot develop an antibedbug mattress because of Mealy's patented technology. Should Mealy develop and release its antibedbug mattress?

Use the following to answer question: Table 12.35 -(Table 12.35)

Use the following to answer question: Table 12.28 -(Table 12.28)

Esther and Eugene hope to be roommates and are choosing between two apartments. Their payoffs are as given in the table. a. What are the pure-strategy Nash equilibria if any? b. What is the mixed-strategy Nash equilibrium?

Suppose two players use strategies that produce these payoffs: a. What are the pure-strategy Nash equilibria if any? b. What is the mixed-strategy Nash equilibrium?

Consider the following game. Either of the two players can choose to stop the game or continue it at any point. If a player continues the game, she loses $1, and $2 is added to her opponent's payoff. The game is played for 10 rounds. Construct the decision tree for this game.

Use the following to answer question: Table 12.15 -(Table 12.15) The table shows the strategies of two players playing prisoner's dilemma. What is player A's strategy?

Use the following to answer question: Table 12.19 -(Table 12.19) The payoffs represent profits in thousands of dollars. Which of the following statements is (are) TRUE?

Suppose the payoffs for players A and B, given their respective strategies, are as in the table: a. What are the pure-strategy Nash equilibria if any? b. What is the mixed-strategy Nash equilibrium?

Jane and Jan are deciding whether to reserve a vacation room with a city view or an ocean view. Their payoffs in terms of their happiness are as follows. a. What are the pure-strategy Nash equilibria if any? b. What is the mixed-strategy Nash equilibrium?

Use the following to answer question: Figure 12.12 -(Figure 12.12) a. What is the Nash equilibrium of this game? b. Is it credible for the United States to threaten to blow up the world if China invades Taiwan?

Use the following to answer question: Table 12.17 -(Table 12.17) The payoffs represent profits in millions of dollars. In this infinitely repeated game, Firm A and Firm B agree to cooperate and not offer warranty coverage. Each firm follows a grim trigger strategy. At what value of d is Firm A indifferent between keeping the agreement with Firm B and cheating on it?

Use the following to answer question: Table 12.33 -(Table 12.33) Two firms have formed an agreement to restrict output. They are playing an infinitely repeated game in which output decisions must be made every period. Both firms are using grim trigger strategies.

Use the following to answer questions 26-28: Table 12.16 -(Table 12.16) The payoffs represent profits measured in thousands of dollars. In this infinitely repeated game, Firm A and Firm B are both using grim trigger strategies; they agree to charge a high price in period 1. If Firm A has a change of heart and decides not to charge a high price in period 1, what is Firm A's expected payoff from cheating? Assume that d = 0.9.

Use the following to answer question: Figure 12.5 -(Figure 12.5) The outcome of this game is for:

Use the following to answer question: Table 12.23 -(Table 12.23)