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Consider the following calculation of Nash equilibria from Wikipedia:

                  Player B plays H  Player B plays T Player A plays H    −1, +1          +1, −1 Player A plays T    +1, −1          −1, +1  To compute the mixed strategy Nash equilibrium, assign A the probability p of playing H and (1−p) of playing T, and assign B the probability q of playing H and (1−q) of playing T.  E[payoff for A playing H] = (−1)q + (+1)(1−q) = 1−2q E[payoff for A playing T] = (+1)q + (−1)(1−q) = 2q−1 E[payoff for A playing H] = E[payoff for A playing T] ⇒ 1−2q = 2q−1 ⇒ q = 1/2 

We have calculated the strategy for player 2, but we haven't used their payoffs, only those for player 1! How is this possible?

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    That seems to be a badly phrased exercise which implicitly relies on being a zero-sum game.2012-04-10

2 Answers 2