Suppose Raphael and Susan 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 Raphael chooses Right and Susan chooses Right, Raphael will receive a payoff of 3 and Susan will receive a payoff of 7.

Susan

Left Right

Raphael Left 4, 6 6, 8

Right 7, 5 3, 7

The only dominant strategy in this game is for to choose . The outcome reflecting the unique Nash equilibrium in this game is as follows: Raphael chooses and Susan chooses

Please refer to Explanation

Explanation:

The Dominant Strategy in a game is the strategy that a player will choose that will provide them with the highest payoff regardless of what the other player does.

In the above, the dominant strategy will be for RAPHAEL to choose LEFT.

By choosing left Raphael makes a payoff of 4 if Susan picks Left as well and a Payoff of 6 if Sudan picks Right. This is better than him picking Right and he will get a Payoff of 3 if Susan chooses Right as well.

The Nash Equilibrium is the strategy where both are making the best that they can given the strategy of the other player and deviating from it will give them less pay out.

The dominant strategy therefore is for RAPHAEL to choose LEFT and for SUSAN to choose RIGHT.

This is because Raphael will pick Left as it maximises their payoff and Susan will then pick a strategy that gives her the highest payoff based on Raphael's decision which is to go RIGHT.

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