Suppose Tim and Alyssa are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Tim chooses Right and Alyssa chooses Right, Tim will receive a payoff of 9 and Alyssa will receive a payoff of 5.

Alyssa

Left Right

Tim Left 6, 6 8, 5

Right 3, 6 9, 5

The only dominant strategy in this game is for to choose .

The outcome reflecting the unique Nash equilibrium in this game is as follows: Tim chooses and Alyssa chooses

Alyssa

Left Right

6,6 8,5

3,6 9,5

1. The only dominant strategy in this game is for Alyssa to choose left.

2. Tim chooses right and Alyssa chooses right.

Explanation:

A dominant strategy is that strategy that always provides the best outcome for a player regardless of what the opponent's strategy is.

Nash equilibrium is a set of strategies, one for each player, such that no player has incentive to change his or her strategy given what the other players are doing.

Now in this game, the dominant strategy is for Alyssa to choose left. If Tim chooses left Alyssa will choose left to earn a payoff of 6. If Tim chooses right the Alyssa will still choose left to earn a payoff of 6. Whatever strategy Tim uses, Alyssa continues to pick left.

Let us consider if there's a dominant strategy for Tim. When Alyssa chooses left Tim chooses left to earn a higher payoff of 6 instead of 3. If Alyssa chooses right then Tim will choose right to earn a payoff of 9 which is higher than 8 (if he had chosen left), we can therefore conclude Tim has no dominant strategy, as his decisions are based on what Alyssa does.

The outcome reflecting the unique Nash equilibrium in this game is as follows: Tim chooses right and Alyssa chooses right. There's no incentive to change at this point.

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