Chapter 11, Problem 1EA

Since they like to eat out, each prefers a restaurant meal to the frozen dinner, but they enjoy their favorite food much more than the other type. Suppose that Linda and Mel have the following payoff matrices, where the numbers represent degree of enjoyment:

Does either player have a dominated strategy? How should they resolve their dilemma?

To determine

Whether there is a dominated strategy of either player or not.

Answer to Problem 1EA

Solution: No player has a dominated strategy.

Explanation of Solution

Given: Payoff matrix of person L,

$\left[\begin{array}{cc}5& 0\\ 0& 2\end{array}\right]$

And the payoff matrix of M,

$\left[\begin{array}{cc}2& 0\\ 0& 5\end{array}\right]$

Each player has two strategies, C for Chinese restaurant and F for a French restaurant.

Explanation:

A dominated strategy is the strategy that always gives a player lesser payoff than other strategies, given whatever other player does.

In this case, no strategy is dominated by another strategy for either player. The dilemma is resolved by choosing either of the Nash equilibrium, which is both players going to either a Chinese or French restaurant.

Conclusion: No dominated strategy exists for either player.