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# cmserver2 - Question 1 The following game appeared in...

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Question 1: The following game appeared in Jacek’s guest lecture regarding a game theoretic analysis of the Cuban Missile Crisis: (a) What is the dominant strategy equilibrium of this game? (b) Is the equilibrium outcome predicted in this game (which you gave in (a)) the same as the real-world result (which was that USA did not attack, USSR did not attack)? If they were not the same, explain why not. Don’t Attack Attack Don’t Attack Attack USSR gets USSR gets USSR gets USSR gets USA gets USA gets USA gets USA gets 0 5 -5 -3 0 -5 5 -3 USSR USA

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Question 2: Consider the following scenario. There are two firms (Domino’s, Mike’s Pizza). Mike’s decides whether or not to enter the market. Domino’s decides what price to set. The resulting payoffs are as follows: If Domino’s plays P1 and Mike’s Enters: Domino’ s gets 2 units, Mike’s gets -1 unit. If Domino ’s plays P1 and Mike’s Stays Out : Domino’ s gets 3 units, Mike’s gets 0 units. If Domino’ s plays P2 and Mike’s Enters: Domino’ s gets 3 units, Mike’s gets 2 units. If Domino’s plays P2 and Mike’s Stays Out: Domino’ s gets 6 units, Mike’s gets 0 units. (a) Fill out the following payoff matrix using the information above. (b) Find all Nash Equilibria for this game. Justify your answer. Enter Stay Out Price 1 Price 2 Mike Dom gets payoff: Mike’s Pizza Domino’s Gets payoff: Dom gets payoff: Dom gets payoff: Dom gets payoff: Mike Mike Mike Gets payoff: Gets payoff: Gets payoff:
Question 3: Consider the following situation. You cohabitate a small apartment with your roommate. You both like living in a clean environment, but neither enjoy cleaning. Therefore you both have symmetric preferences defined by the following ordering: 1) Your roommate cleans the apartment 2) You both clean the apartment together 3) You clean the apartment alone 4) Neither of you clean the apartment You would like to model this problem as a strategic game. a) List the players of the game b) List the strategies of the players c) Create a matrix of payoffs (clearly labeling players and strategies) consistent with the preferences defined above. d) Does either player have one or more dominant strategies? If so, what is it/are they? e) What are the Nash equilibria(ium) of the game?

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cmserver2 - Question 1 The following game appeared in...

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