Exam 12: Game Theory

(Table: Detroit Art School and Motor City Art School I) The payoffs represent profits measured in thousands of dollars. In this infinitely repeated game, the two schools agree to cooperate and not offer financial aid. Each school follows a grim trigger strategy. At what value of d is the Motor City Art School indifferent between upholding and cheating on the agreement?

(Table: Players 1 and 2 I) The table shows the payoffs from the game rock-paper-scissors. Which of the following statements is (are) TRUE? I. There is no pure-strategy Nash equilibrium. II. The Nash equilibria are (rock, rock), (paper, paper), and (scissors, scissors). III. The mixed-strategy Nash equilibrium is for each player to randomly select each strategy one-third of the time.

(Table: Polaris and Yamaha I) The payoffs represent profits in millions of dollars. Suppose that this simultaneous-move game is played once in each period for three periods. In period one, the outcome will be _____, and in period two, the outcome will be _____.

(Table: Lemonade) Andrei and Sonya operate lemonade stands in the same neighborhood. Payoffs are in quarters . This can also be extended: c + ad + cd² + ad³. . . = (c + ad)/(1 - d²).

(Table: Sports Illustrated and ESPN Magazines I) Payoffs represent profits in millions of dollars. In a Nash equilibrium, Sports Illustrated will run the _____ cover story and ESPN Magazine will run the _____ cover story.

(Table: Players 1 and 2 IV) a. Is there a pure-strategy Nash equilibrium? b. Is there a mixed-strategy Nash equilibrium?

Consider two players with the following decision tree. What is the Nash equilibrium?

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 Denise chooses biking with a probability of ____.

Suppose that in a two-player game in which 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 is a pure-strategy Nash equilibrium at ____.

Consider the following game. Find the mixed-strategy Nash equilibrium.