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In the classic introduction to non-cooperative game theory, the mixed strategy for a player is taught as a distribution over strategy space for the player. The distribution essentially gives us the probabilities (say, discrete strategy set) with which a player should play the strategies in a Nash equilibrium.
However probabilities carry the notion of being frequencies and these essentially mean the long-run fraction of games in which the player should play the strategy. However the setting is a one-shot game and this is a contradiction.
How do we resolve the contradiction when explaining what a mixed strategy is?
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