pr9c.zerosum - Zero-Sum Games Part C: Mixed Strategies, 2xn...

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Zero-Sum Games Part C: Mixed Strategies, 2xn games 2 ECON 461 Spring 2010, H. Ofek Zerosum Games Approach to games larger than 2 x 2 A mixed strategy in a game larger than 2x2 may generally assign zero probability to one (or more) of the pure strategies. The following rules of thumb are useful to bear in mind when it comes to the assignment of probabilities (zero or non-zero) to pure strategies. 1. A mixed strategy is a best response to a rival action if and only if each of the pure strategies to which it assign positive probability is also a best response to the same rival action. Consequently, 2. A rational player who chooses to play a mixed strategy will always be indifferent among all the pure strategies to which the mixed strategy assigns positive probability.
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3 ECON 461 Spring 2010, H. Ofek Zerosum Games Ex. 3: Step 1 t 1 t 2 t 3 s 1 5 0 1 0 maximin s 2 2 7 4 2 max 574 minimax min Since maximin = 2 4 = minimax , the game has no value in pure strategies. Nor does it have a pure-strategy Nash equilbrium.
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pr9c.zerosum - Zero-Sum Games Part C: Mixed Strategies, 2xn...

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