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Respond to the question: A better Nash equilibrium?

07/21/2016 09:43 AM by EstEst; A ,,better'' Nash equilibrium?
Consider a game where two players (1,2) chooses between two strategies (A,B). The payoff vectors are: p(A,A)=(1,0), p(B,B)=(0,0), p(A,B)=(2,2), p(B,A)=(2,2).
There are clearly 2 Nash equilibria ((A,B) and (B,A)), but intuitively, only (A,B) should be the rational solution: player 1 does not know about the strategy of player 2 so he has to guess it: while he guesses correctly, he always gets payoff 2, but when he fails to guess, he is better off guessing A. Therefore, choosing A is a better answer for player 1 and player 2 knows it, so he chooses B. Is there any formal way to solve this game and generally to tell apart one Nash equilibrium from the other like in this example? [Manage messages]