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Suppose Alex and Becky 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 Alex chooses Right and Becky chooses Right, Alex will receive a payoff of 5 and Becky will receive a payoff of 5.

Becky

Left Right

Alex Left 6, 6 6, 3

Right 4, 3 5, 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:

Alex chooses______ and Becky chooses_______ .

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Answer:

The only dominant strategy in this game is for__Alex_ to choose__Right___ .

The outcome reflecting the unique Nash equilibrium in this game is as follows:

Alex chooses__Right____ and Becky chooses__Left_____ .

Explanation:

The game theory of the Nash equilibrium achieves the optimal outcome of a game because Alex and Becky are not incentivized to deviate from their chosen strategies after considering the opponent's choice.  Neither of these two players can increase their payoff by choosing an action different from their current strategic action. Thus, this action profile achieves a Nash equilibrium for the two players because there exists randomization in the game.

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