a3 - Fahad Khalil Answer Key 3 Econ 485 For 2 person games...

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Fahad Khalil Econ 485 Answer Key 3 For 2 person games with 3 pure strategies, we will prove that a player will never use a strictly dominated strategy with a positive probability in a NE. This proof can be applied for strategy sets with two pure strategies also. (c 1 ) (c 2 ) (1-c 1 -c 2 ) L C R (r 1 ) T x 1 , - x 2 , - x 3 , - (r 2 ) M y 1 , - y 2 , - y 3 , - (1 - r 1 - r 2 ) B -, - -, - -, - We know that strictly dominated strategies are not used in NE if only pure strategy NE are considered. Here we show that the same is true even when mixed strategies are considered. Only the Row player's payoffs for T and M are needed for this proof. The other payoffs are not really relevant, but you can put in any if you want. Suppose T strictly dominates M for Row. Then, x 1 > y 1 , x 2 > y 2 , and x 3 > y 3 . If Row plays T with probability 1 while Column plays with probability c = (c 1 , c 2 , 1 - c 1 - c 2 ), then Row's expected payoff is: U R (r 1 =1, c) = c 1 ·x 1 + c 2 ·x 2 + (1 - c 1 - c 2
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a3 - Fahad Khalil Answer Key 3 Econ 485 For 2 person games...

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