# Consider a game where player 1 has three strategies (T, M, B)

Consider a game where player 1 has three strategies (T, M, B) and player 2 has two strategies (L, R). Player 2 plays L with probability q, and consequently R with probability (1 ( q). Player 1 is trying to compare the payoff from playing the pure strategy B with the payoff from playing T with probability p and M with probability (1 ( p). The payoffs to player 1 are given below: L RT 3, __ 0, __M 0, __ 3, __B 2, __ 2, __ With player 2 playing a (q, 1 ( q) mix of strategies L and R, when will player 1 receive a higher payoff from a (p, 1 ( p) mix of strategies T and M than from strategy B? To answer this question in the most general way possible, you shouldCalculate an expression for player 1’s payoff as a function of p and q. Remember that player 1 is using a (p, 1 ( p) mix of strategies T and M and player 2 is using a (q, 1 ( q) mix of strategies L and R.Use this expression to obtain conditions under which the (T, M) mix will provide player 1 with a higher payoff than B will as a pure strategy. These conditions involve comparing p to a certain function f(q).Graph f(q) vs. q with relative accuracy. Use your graph to show what combinations of p and q will result in a higher payoff to player 1 from the (T, M) mix than from the pure strategy B.Provide a specific combination of p and q for which player 1 receives a lower payoff from the (T, M) mix than from the strategy B.

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