Suppose Jacques and Kyoko 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 Jacques chooses Right and Kyoko chooses Right, Jacques will receive a payoff of 5 and Kyoko will receive a payoff of 3. Kyoko
Left Right
Jacques Left 4, 4 6, 3
Right 5, 4 5, 3

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

The only dominant strategy in this game is for Kyoko to choose Left. The outcome reflecting the unique Nash equilibrium in this game is as follows: Jacques chooses Right and Kyoko chooses Left.

Explanation:

A dominant strategy is strategy that makes a player better off regardless of the strategy of his opponents in a game.

From the payoff matrix, it can be observed that, when Jacques plays Left, Kyoko will also play Left because 4 > 3. But, when Jacques plays Right, Kyoko will still play Left because 4 > 3. This indicated that Kyoko will always play Left no matter what Jacques plays. As a result, the dominant strategy for Kyoko is Left.

On the other hand, when Kyoko plays Left, Jacques will play Right because 5 > 4. But when Kyoko plays Right, Jacques will play Left because 6 > 5. This shows that Jacques does not have any particular strategy that make him better off. As a result, Jacques does not have a dominant strategy.

Based on the above analysis, we have:

The only dominant strategy in this game is for Kyoko to choose Left. The outcome reflecting the unique Nash equilibrium in this game is as follows: Jacques chooses Right and Kyoko chooses Left.

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