3. Consider a two-player Rock-Paper-Scissors game: rock beats scissors, scissors beat paper, paper beats rock (this is another zero-sum game). Find pure strategy and mixed strategy nash equilibrium. Suppose winning gives player payoff of 1 and losing results in -1 payoff, in case of tie both get zero. Lets add one more strategy called Dynamite. Dynamite beats everything, but if both players choose it, they end up in the hospital, payoff -10,000 for both. Discuss how adding this new strategy affects the equilibrium outcomes of the game.

3. Consider a two-player Rock-Paper-Scissors game: rock beats scissors, scissors beat paper, paper beats rock (this is another zero-sum game). Find pure strategy and mixed strategy nash equilibrium. Suppose winning gives player payoff of 1 and losing results in -1 payoff, in case of tie both get zero. Lets add one more strategy called Dynamite. Dynamite beats everything, but if both players choose it, they end up in the hospital, payoff -10,000 for both. Discuss how adding this new strategy affects the equilibrium outcomes of the game.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.3P

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. Find the Nash equilibrium of the following modified Rock-Paper-Scissors game: • When rock (R) beats scissors (S), the winner’s payoff is 10 and the loser’s payoff is −10. • When paper (P) beats rock, the winner’s payoff is 5 and the loser’s payoff is −5. • When scissors beats paper, the winner’s payoff is 2 and the loser’s payoff is −2. • In case of ties, both players receive 0 payoff. You are suposed to create a system of equations and then solve for them and find 3 probabilities- please show how to do that
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Hi this is from a textbook. Thank you. Consider the following game in which Sally can play T or B and John chooses between L or R. Each player makes their choice simultaneously. If Sally chooses T and John chooses L, Sally gets a payoff of 5 and John has a payoff of 4. If Sally plays T and John R, Sally’s payoff is 8 and John gets 3. If Sally Chooses B and John L, the payoffs are 3 to Sally and 2 to John. Finally, if Sally chooses B and John R, the payoffs are 7 to Sally and 0 to John. Which statement is true? a) The Nash equilibrium is (B,R); this is a prisoners’ dilemma b) The Nash equilibrium is (T,R); this is a prisoners’ dilemma c) The Nash equilibrium is (T,R); this is not dominant strategy equilibrium d) The Nash equilibrium is (T,L); this is a dominant strategy equilibrium e) None of the above
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