Consider the 2-player, zero-sum game "Rock, Paper, Scissors". Each player chooses one of 3 strategies: rock, paper, or scissors. Then, both players reveal their choices. The outcome is determined as follows. If both players choose the same strategy, neither player wins or loses anything. Otherwise: "paper covers rock": if one player chooses paper and the other chooses rock, the player who chose paper wins and is paid 1 by the other player. "scissors cut paper": if one player chooses scissors and the other chooses paper, the player who chose scissors wins and is paid 1 by the other player. • "rock breaks scissors": if one player chooses rock and the other player chooses scissors, the player who chose rock wins and is paid 1 by the other player. We can write the payoff matrix for this game as follows: scissors rock paper -1 rock 0 paper 1 0 scissors -1 1 -1 2. Suppose now we alter the game so that whenever Colin chooses "paper" the loser pays the winner 3 instead of 1: rock paper scissors -3 1 rock 0 paper 1 0 scissors (a) Show that x¹=(.) and yT=(..) together are not a Nash equilibrium for this modified game.
Consider the 2-player, zero-sum game "Rock, Paper, Scissors". Each player chooses one of 3 strategies: rock, paper, or scissors. Then, both players reveal their choices. The outcome is determined as follows. If both players choose the same strategy, neither player wins or loses anything. Otherwise: "paper covers rock": if one player chooses paper and the other chooses rock, the player who chose paper wins and is paid 1 by the other player. "scissors cut paper": if one player chooses scissors and the other chooses paper, the player who chose scissors wins and is paid 1 by the other player. • "rock breaks scissors": if one player chooses rock and the other player chooses scissors, the player who chose rock wins and is paid 1 by the other player. We can write the payoff matrix for this game as follows: scissors rock paper -1 rock 0 paper 1 0 scissors -1 1 -1 2. Suppose now we alter the game so that whenever Colin chooses "paper" the loser pays the winner 3 instead of 1: rock paper scissors -3 1 rock 0 paper 1 0 scissors (a) Show that x¹=(.) and yT=(..) together are not a Nash equilibrium for this modified game.
Chapter15: Imperfect Competition
Section: Chapter Questions
Problem 15.7P
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