Consider the familiar Rock, Paper, Scissors game. Two players indicate either Rock, Paper, or Scissors simultaneously....

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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 paper The loser gets a payoff of -1 and the winner gets +1. If both players choose the same, both of them gets 0. 1. Write down the (payoff) matrix of the game. Does either player has a dominant strategy? If the game has one or more pure-strategy Nash equilibrium, find all of them. If the game does not have a pure-strategy Nash equilibrium, explain why. 2. Now consider a different set of rules to determine the winner: • Rock crushes scissors • Rock flies right through paper (Rock beats paper) • Scissors cut paper Write down the (payoff) matrix of the new game. Does either player has a dominant strategy? If the new game has one or more pure-strategy Nash equilibria, find all of them. If the new game does not have a pure-strategy Nash equilibrium, explain why. 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 paper The loser gets a payoff of -1 and the winner gets +1. If both players choose the same, both of them gets 0. 1. Write down the (payoff) matrix of the game. Does either player has a dominant strategy? If the game has one or more pure-strategy Nash equilibrium, find all of them. If the game does not have a pure-strategy Nash equilibrium, explain why. 2. Now consider a different set of rules to determine the winner: • Rock crushes scissors • Rock flies right through paper (Rock beats paper) • Scissors cut paper Write down the (payoff) matrix of the new game. Does either player has a dominant strategy? If the new game has one or more pure-strategy Nash equilibria, find all of them. If the new game does not have a pure-strategy Nash equilibrium, explain why.

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1 a Payoff matrix of the game Rock Paper Scissors Rock 0 1 1 Paper 1 0 1 Scissors 1 1 0 In this matrix the rows represent Player 1s choices and the columns represent Player 2s choices The numbers in t... View the full answer