Suppose Yakov and Ana 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 Yakov chooses Right and Ana chooses Right, Yakov will receive a payoff of 8. Ana
Left Right
Yakov Left 8,5 8,7
Right 3,6 9,8
a. The only dominant strategy in this game is for to choose .
b. The outcome reflecting the unique Nash equilibrium in this game is as follows: Yakov chooses and Ana chooses .

a. The only dominant strategy in this game is for Ana to choose Right.

b. The outcome reflecting the unique Nash equilibrium in this game is as follows: Yakov chooses Right and Ana chooses Right.

Explanation:

A dominant strategy is one that makes a player better off regardless of the choices made by his or her opponent in a game.

Given:

                                 Ana

                         Left            Right

Yakov  Left       8,5               8,7

            Right    3,6               9,8

In this game, when Yakov plays Left, Ana will choose Right since 7 > 5. Ana will also choose Right when Yakov plays Right since 8 > 6. This demonstrates that Ana will always play Right, regardless of what Yakov does. This means that Ana's dominant strategy is Right.

On the other hand, when Ana plays Left, Yakov will also play Left because 8 > 3. However, because 9 > 8, when Ana plays Right, Yakov will likewise play Right. This demonstrates that Yakov does not have a specific strategy that makes him better off. As a result, Yakov lacks a dominant strategy.

Based on the above analysis, we have:

a. The only dominant strategy in this game is for Ana to choose Right.

b. The outcome reflecting the unique Nash equilibrium in this game is as follows: Yakov chooses Right and Ana chooses Right.