Question

Suppose Charles and Dina 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 Charles chooses Right and Dina chooses Right, Charles will receive a payoff of 7 and Dina will receive a payoff of 4.

Dina
Left Right
Charles Left 6,3 6,4
Rigt 3,3 7,4

Required:
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: Charles chooses_______ and Dina choose ______

Answer 1

Answer and Explanation:

As per the data given in the question,

a) Dominant strategy is that strategy in which a player chooses strategy irrespective of the strategy which other player has already chosen.

For Charles, If Dina chooses right he will choose right because payoff is higher (6 > 3) but if Dina chooses left he will choose left because payoff is

is higher (7>6) So, he doesn't have any strategy.

For Dina, he will choose right because it gives highest payoff whether Charles choose right or left.

The dominant strategy is for Dina to choose right.

b)

The outcome matching the unique Nash equilibrium in this game is :

Nash equilibrium is that in which both players will chose after keeping in mind the other players' strategy.

Here equilibrium is :

Charles chooses right(while Dina chooses Right) and Dina chooses right (while Janet chooses right).