Find the optimal strategies, P and Q, for the row and column players, respectively. Fractions should be reduced, but not written as mixed numbers. Do not use decimal answer -1 6 -7 P= Q= Compute the expected payoff E of the matrix game if the players use their optimal strategies. (Round your answer to two decimal places.) E = Which player does the game favor, if any? OR O O neither

Find the optimal strategies, P and Q, for the row and column players, respectively. Fractions should be reduced, but not written as mixed numbers. Do not use decimal answer -1 6 -7 P= Q= Compute the expected payoff E of the matrix game if the players use their optimal strategies. (Round your answer to two decimal places.) E = Which player does the game favor, if any? OR O O neither

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Game Theory de Drew Fudenberg, Jean Tirole. Exercise 2.6**
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Mixed Nash Equilibrium Player 2 C D A 5,1 1,3 B 2,6 4,2 PLAYER 1 a) calculate the probability In equilibrium Player 1 chooses A with probability a= [?] and player 2 chooses M with probability B = [ ?] b) calculate payoff for mixed strategy nash equilibrium Player 1 gets payoff of [?] Player 2 gets payoff of [?] c) Suppose the payoff for (B,C) would change to (0,8) Would probability a increase,decrease, stay the same? Would probability B increase,decrease, stay the same?
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Define a new game as a modified version of the game in Problem 1, which we will call the Matching Two Pennies game: each player choose heads (H) or tails (T) for two pennies. In this game, Player 1 wins if both coins show the same combination of heads and tails, while Player 2 wins if they do not. (a) Write the strategy sets S1 and S2 for this game. (b) Give the payoffs for each player in this Matching Two Pennies game, by defining T;(81, 82) for each player and for each strategy pair, either as a list or in matrix form.
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