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Game Theory and Applications following H. Varian Chapters 28 & 29

Game Theory and Applications following H. Varian Chapters 28 & 29. Defining a Nash Equilibrium The situation when Player A's choice is optimal for him given Player B's choice; and Player B's choice at the same time is optimal for him given Player A's choice.

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Game Theory and Applications following H. Varian Chapters 28 & 29

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  1. Game Theory and Applications following H. Varian Chapters 28 & 29

  2. Defining a Nash Equilibrium The situation when Player A's choice is optimal for him given Player B's choice; and Player B's choice at the same time is optimal for him given Player A's choice. Or: A pair of strategies (r*,c*) such that c*=bc(r*) and r*=br(c*), where c* is Player B's best response, and r* is Player A's best response, and b is a function that chooses the best response for player i=r,c.

  3. Mixed Strategies:

  4. Let r be the probability that "Row" plays Top and let c be the probability that "Column" plays Left. Row's payoff= 2rc + 1 -r - c +rc; In changes: RowPay=(3c-1)r Col's payoff=cr +2(1-c)(1-r); In changes: ColPay=(3r-2)c

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