Exam 12: Game Theory

Suppose the payoffs for players A and B, given their respective strategies, are as in the table: There is a mixed-strategy Nash equilibrium when Player A chooses Down with probability ____.

Kelly and Karl can vote for or against a public project. Their payoffs are given in the table: There is a pure-strategy Nash equilibrium at ____.

(Table: Hanes and Fruit of the Loom T-Shirts II) Answer the following. a. In Table A, identify the Nash equilibria. b. In Table B, identify the Nash equilibria.

The following game has _____ pure-strategy equilibrium (equilibria) and (but) _____ mixed-strategy equilibrium.

(Table: Firms 1 and 2 I) Payoffs represent profits measured in thousands of dollars. Which of the following outcomes represent(s) a Nash equilibrium? I. (200 , 200) II. (600 , 990) III. (650, 400) IV. (400 , 825)

(Table: Players A and B II) The table shows the strategies of two players playing prisoner's dilemma. What is player A's strategy?

Consider two players in the following game. For what values of the discount rate would a grim trigger strategy ensure cooperation between the two players if they play forever?

Which of the following statements about mixed strategies is FALSE?

Suppose that, in a two-player game, player A can move Up or Down, and player B can choose Left or Right. Payoffs for this game are given in the table. a. What are the pure-strategy Nash equilibria if any? b. What is the mixed-strategy Nash equilibrium?

The _____ model is an example of a simultaneous game, while the _____ model is an example of a sequential game.

Suppose the payoffs for players A and B, given their respective strategies, are as in the table: There is a mixed-strategy Nash equilibrium when Player B chooses Right with probability ____.

(Table: Firms A and B VIII) a. In a one-period simultaneous game, what is the Nash equilibrium? b. If this simultaneous game is played twice, once in each period, what will be the outcome in the first period? In the second period?

(Table: Firms 1 and 2 IV) Payoffs represent profits in millions of dollars. The Nash Equilibrium in this game is ____.

Suppose that, in a two-player game, player A can move Up or Down, and player B can choose Left or Right. Payoffs for this game are given in the table: There exists a mixed-strategy Nash equilibrium at which Player A plays Up with probability ____.

(Table: Jack and Jill I) If Jack chooses to not climb the hill and Jill brings the pail, Jill's payoff is ____.

Dennis and Denise are trying to decide whether to go hiking or biking this weekend. Depending on their choices, they might go together or they might go apart. Their payoffs in terms of their happiness are as follows. There exists a mixed-strategy Nash equilibrium when Dennis chooses biking with a probability of ____.

Robert and Rosalie are deciding whether to request fish or chicken at a wedding that they will attend. If they order different meals, they can try each of the dishes by sharing. Their payoffs in terms of their happiness are as follows. There is a pure-strategy Nash equilibrium at ____.

Consider the following game. The choices of ____ represent a Nash Equilibrium in this game.

(Table: Lemonade) Answer the following questions. a. Who are the players? b. What strategies does each player have? c. Identify any dominant strategies.

Which of the following statements is (are) TRUE? I. A Nash equilibrium requires that each player have a dominant strategy. II. A Nash equilibrium requires that each player have a dominated strategy. III. A game can have more than one Nash equilibrium.