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[solution] » Consider a strategic game G = (S1,...,Sn;u1,...,un). 1. Suppose p

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Consider a strategic game G = (S1,...,Sn;u1,...,un). 1. Suppose p

  Consider a strategic game G = (S1,...,Sn;u1,...,un).
1. Suppose p and q are strategies for player 1, and let ? ? [0,1]. Show that ?p + (1??)q is also a strategy for player 1. 

2. More generally, show that any convex combination of strategies is again a strategy.

3. A strategy p for player 1 is optimal with respect to strategies p2, ..., pn for the other players, if it maximizes the expected payo? for player 1. Prove that a convex combination of optimal strategies is again optimal


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