Even if a game has pure strategy Nash equilibria, it might be that none of those pure strategies are ESS . Consider the Hawk-dove game and Best response for explanation ).
32.
There is no contradiction because in this case neither player is restricted to absolutely continuous distributions ( and the demonstration that the game has no value requires both players to use pure strategies ).
33.
The Intimate Apparel Council says the panty raid was pure strategy designed to draw the eyes of the world media, already focused on New York to look at clothes, to what typically goes unseen.
34.
Thus it should depend only on the reduced normal-form game obtained after elimination of pure strategies that are redundant because their payoffs for all players can be replicated by a mixture of other pure strategies.
35.
If there is a stable average frequency with which each pure strategy is employed by the " average member " of the appropriate population, then this stable average frequency constitutes a mixed strategy Nash equilibrium.
36.
Thus it should depend only on the reduced normal-form game obtained after elimination of pure strategies that are redundant because their payoffs for all players can be replicated by a mixture of other pure strategies.
37.
Mixed strategies are still widely used for their capacity to provide Nash equilibria in games where no equilibrium in pure strategies exists, but the model does not specify why and how players randomize their decisions.
38.
The mixed strategy equilibria are explained as being the limit of pure strategy equilibria for a disturbed game of incomplete information in which the payoffs of each player are known to themselves but not their opponents.
39.
The game is one of pure strategy; outside of the " Confusion " spell which causes a random gesture to be made all spell effects can be anticipated deterministically, making it akin to Chess or Go.
40.
Often a card game is described as " pure strategy " and such, but a game with any sort of random shuffling or face-down dealing of cards should not be considered to be " no chance ".
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