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Use the following payoff matrix for a siμltaneous-move one-shot game to answer the accompanying questions.

beginarrayc|cccc & textPlayer 2 hline textPlayer 1 & a & b hline c & 11, 23 & 21, 10 d & 28, 14 & 29, 12 e & 15, 4 & 12, 14 f & 19, 25 & 18, 18 endarray

a) What is the optimal strategy for Player 1?
b) What is the optimal strategy for Player 2?
c) What is the Nash equilibrium for this game?
d) If Player 1 plays strategy b, what should Player 2 do?

User Peter Zhao
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Final answer:

The optimal strategy for Player 1 is strategy c, while the optimal strategy for Player 2 is strategy b. The Nash equilibrium is (c, b). If Player 1 plays strategy b, Player 2 should choose strategy d.

Step-by-step explanation:

To determine the optimal strategy for Player 1, we need to analyze the payoff matrix. The optimal strategy is the one that maximizes Player 1's payoff regardless of what Player 2 chooses. By examining the payoffs for each strategy, we can see that Player 1 should choose strategy c, as it provides the highest payoff of 28 when Player 2 chooses strategy d.

To determine the optimal strategy for Player 2, we need to look at the payoffs for each of their strategies. By examining the payoffs, we can see that Player 2 should choose strategy b, as it provides the highest payoff of 29 when Player 1 chooses strategy d.

The Nash equilibrium occurs when both players are choosing their optimal strategies. In this case, the Nash equilibrium is (c, b), where Player 1 chooses strategy c and Player 2 chooses strategy b.

If Player 1 plays strategy b, Player 2 should choose strategy d, as it provides the highest payoff of 29.

User AhmadAssaf
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