1. IDSDS. (5 points) Two students, Jessie and James, are suspected for cheating during an exam. The principal separates Jessie and James into a separate room for an investigation. If both students deny, then both students are suspended for a week. If one student admits and the other denies, then the student who admits, is given no suspension, while the other is suspended for 4 weeks. If both students admit, then each student is suspended for two weeks. The game can be represented in the following table: James admit deny Jessie admit -2, -2 0, -4 deny -4, 0 Find the outcome of the game using IDSDS. 2. Finding the Nash Equilibrium. (5 points) Consider a baseball game between a pitcher and a batter. The pitcher can either throw a fast or curve ball. The batter can choose to swing or not swing. The game and its payoffs can be represented in the following table: Batter swing not swing Pitcher fast -5, 5 5,0 curve -2, 3 3, 2 (a) Explain the pitcher's best responses. Does the pitcher have any dominated strategies? (b) Explain the batter's best responses. Does the batter have any dominated strate- gies? (c) What is the pure strategy Nash Equilibrium? 3. Finding the Nash Equilibrium. (10 points) Consider a penalty game in soccer. The kicker has the options of kicking left, right, or middle. Similarly, the goalkeeper has the options of jumping to the left or right, or staying in the middle. If the kicker chooses the same direction as the goalkeeper, the kicker gets -1 payoff and the goalkeeper gets a payoff of 1. Otherwise, the kicker receives a payoff of 1 and the goalkeeper receives a payoff of -1. Washington State University School of Economic Sciences Goalkeeper L M R L -1,1 1,-1 1,-1 Kicker M 1,-1 -1,1 1,-1 R 1,-1 1,-1 -1,1 (a) Explain the kicker's best responses. (b) Explain the goalkeeper's best responses. (c) Does the game have any pure strategy Nash Equilibria? 4. Sequential Game. (5 points) Let's use the same scenario and payoffs from question 1. (a) Convert the table from question 1 to an extensive form with Jessie as the first mover. (b) Using a backward induction approach, find the outcome of the game with Jessie moving first