7. Solving for dominant strategies and the Nash equilibrium Suppose Lorenzo and

Question

7. Solving for dominant strategies and the Nash equilibrium

Suppose Lorenzo and Neha 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 Lorenzo chooses Right and Neha chooses Right, Lorenzo will receive a payoff of 6 and Neha will receive a payoff of

The only dominant strategy in this game is for (Neha/Lorenzo) to choose (Right/Left)t .

The outcome reflecting the unique Nash equilibrium in this game is as follows: Lorenzo chooses (Right/Left) and Neha chooses (Right/Left) .

                         Neha          Left           Right Lorenzo             Left          8, 4              4, 5             Right          5, 4           6, 5

Explanation / Answer

A dominant strategy is that strategy a player chooses, irrespective of what the other player chooses.

For Lorenzo, if Neha chooses Left, he chooses Left (as payoff is higher: 8 > 5) but if Neha chooses Right, he chooses Right (as payoff is higher: 6 > 4). So, he does not have any dominant strategy.

For Neha, she will choose Right whether Lorenzo chooses Left or chooses Right as that gives the highest payoff (5> 4).

So the only dominant strategy is for Neha to choose Right.

Nash equilibrium is that set of strategy which both players will choose, after considering the other player's strategy. Here, Nash equilibrium is: Lorenzo chooses Right (when Neha chooses Right) and Neha chooses Right (when Lorenzo chooses Right).

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