Solving for dominant strategies and the Nash equilibrium Suppose Nick and Rosa 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 Nick chooses Right and Rosa chooses Right, Nick will receive a payoff of 7 and Rosa will receive a payoff of 6.

Rosa
Left Right
Nick Left 8,4 4,5
Right 5,4 6,5

The only dominant strategy in this game is for ___ to choose _ . The outcome reflecting the unique Nash equilibrium in this game is as follows: Nick chooses _ and Rosa chooses ___ .

The only dominant strategy in this game is for NICK to choose RIGHT. The outcome reflecting the unique Nash equilibrium in this game is as follows: Nick chooses RIGHT and Rosa chooses RIGHT.

Explanation:

ROSA

left right

4 / 6 /

left 3 4

NICK

right 6 / 7 /

7 6

Rosa does not have a dominant strategy since both expected payoffs are equal:

if she chooses left, her expected payoff = 3 + 7 = 10
if she chooses right, her expected payoff = 4 + 6 = 10

Nick has a dominant strategy, if he chooses right, his expected payoff will be higher:

if he chooses left, his expected payoff = 4 +6 = 10
if he chooses right, his expected payoff = 6 + 7 = 13

The only possible Nash equilibrium exists if both Rosa and Nick choose right, so that their strategies are the same, resulting in Rosa earning 6 and Nick 7.