Quiz on Game Theory: Nash Equilibria and Optimal Strategies in a 2x2 Matrix Game - Prof. J, Quizzes of Managerial Economics

Download Quiz on Game Theory: Nash Equilibria and Optimal Strategies in a 2x2 Matrix Game - Prof. J and more Quizzes Managerial Economics in PDF only on Docsity! Finance 30210 Quiz #8 Name________________________ Section________________ 1) Consider the following game (Player one’s payoffs are in bold): Player Two Cooperate Cheat Player One Cooperate $30 $30 $0 $10 Cheat $10 $0 $15 $15 a) What is each player’s optimal strategy? Player #1: If player two cooperates, player 1 should cooperate. If player two cheats, player 1 should cheat. Player #2: Same as player 1. b) Suppose it is known that player two will cooperate, on average, 50% of the time. If player one knows this, how should she respond? If player 1 cheats: ( ) ( ) 5.12155.105. =+ If player 1 cooperates: ( ) ( ) 1505.305. =+ Player 1 will always cooperate. c) Calculate the Nash equilibria for this game. There are two pure strategy equilibria: Cheat Cheat and Cooperate, Cooperate as well as one mixed strategy equilibrium. If player 1 cheats: ( ) ( )1510 Chco PP + If player 1 cooperates: ( ) ( )030 ChCo PP +