mixed-strategy

mixed-strategy - Handout on Mixed Strategies ECN 416,...

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Handout on Mixed Strategies ECN 416, Spring 2010 Main Lesson in class: If a mixed strategy is a best response, then each of the pure strategies involved in the mix must itself be a best response. In particular, each must yield the same expected payo f . Before explaining why this must be true, let’s try to rewrite this formally, using the notation we introduced in class. Formally, if player ’s mixed strategy is a best response to the (mixed) strategies of the other players, , then, for each pure strategy such that ( ) 0 ,itmustbethecasethat is itself a best response to .I n particular,  ¡  ¢ must be the same for all such strategies. Why is this true? Suppose it were not true. Then there must be at least one pure strategy that is assigned positive probability by my best response mix and that yields a lower expected payo f against .I fth e r e is more than one, focus on the one that yields the lowest expected payo f . Suppose I drop that (low-yield) pure strategy from my mix, assigning the weight I used to give it to one of the other (higher-yield) strategies in the mix. This must raise my expected payo
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mixed-strategy - Handout on Mixed Strategies ECN 416,...

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