Introduction to game theory;

1) Consider the following version of the prisoners dilemma game (Player one's payoffs are in bold): Player Two Cooperate Cheat Player One Cooperate $10 $10 $0 $12 Cheat $12 $0 $5 $5 a) What is each player's dominant strategy? Explain the Nash equilibrium of the game.b) Suppose that this game were played three times in a row. Is it possible for the cooperative equilibrium to occur? Explain.2) Consider the familiar "Rock, Paper, Scissors" game. Two players indicate either "Rock", "Paper", or "Scissors" simultaneously. The winner is determined by Rock crushes scissors Paper covers rock Scissors cut paperIndicate a -1 if you lose and +1 if you win. Write down the strategic (matrix) form of the game. What is the Nash equilibrium of the game?3) Consider the following game (Player One's Payouts in bolds): Player 2 Left Middle Right Player 1 Up 1, 2 3, 5 2, 1 Middle 0. 4 2, 1 3,0 Down -1, 1 4, 3 0. 2 a) Does either player have a dominant strategy? Explain.4) Consider the game of chicken. Two players drive their cars down the center of the road directly at each other. Each player chooses SWERVE or STAY. Staying wins you the admiration of your peers (a big payoff) only if the other player swerves. Swerving loses face if the other player stays. However, clearly, the worst output is for both players to stay! Specifically, consider the following payouts. (Player one's payoffs are in bold): Player Two Stay Swerve Player Stay -6 -6 2 -2 One Swerve -2 2 1 1 a) Does either player have a dominant strategy? Explain.b) Suppose that Player B has adopted the strategy of Staying 1/5 of the time and swerving 4/5 of the time. Show that Player A is indifferent between swerving and staying.c) If both player A and Player B use this probability mix, what is the chance that they crash?5) Consider the following game. Two criminals are thinking about pulling off a bank robbery. The take from the bank would be $20,000 each , but the job requires two people (one to rob the bank and one to drive the getaway car. Each criminal could instead rob a liquor store. The take from robing a liquor store is only $1000 but can be done with one person acting alone. a) Write down the payoff matrix for this game