:

The first-order conditions are:

x = 20 y = 40

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| | b1 | b2 | | --- | --- | --- | | a1 | 2, 3 | 1, 2 | | a2 | 3, 1 | 2, 2 |

Solving these conditions simultaneously yields:

Consider a game with two players, A and B. Player A has two strategies, a1 and a2, while player B has two strategies, b1 and b2. The payoff matrix is: