Question

Suppose Darnell and Eleanor 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 Darnell chooses Right and Eleanor chooses Right, Darnell will receive a payoff of 7 and Eleanor will receive a payoff of 2.Darnel Eleanor Left Right Left 6, 5 4,4 Right 5, 3 7, 2The only dominant strategy in this game is for Darnell/Eleanor to choose Left/Right.The outcome reflecting the unique Nash equilibrium in this game is as follows: Darnell chooses Left/Right. and Eleanor chooses Left/Right.

Answer 1

Answer: a) Eleanor picks Left as Dominant strategy

b) Both pick LEFT at Nash Equilibrium.

Explanation:

The Dominant strategy is that strategy that once embarked on, gives the highest benefit irrespective of what the other player does.

The Dominant strategy therefore is for ELEANOR to pick LEFT. Should Eleanor pick left, they stand a chance to gain 5 if Darnel picks Left as well and 3 if Darnel picks Right. This is better than picking Right because there Eleanor has a chance of a Payoff of 2.

The Nash Equilibrium of a game is the point where both players are at their best alternative meaning that it is beneficial to both of them to remain where they are.

With Eleanor always picking Left, it would be beneficial for Darnel to pick Left as well and make a Payoff of 6 which is the highest they can make with Eleanor picking Left.

The Nash equilibrium in this game is as follows: DARNEL chooses LEFT and ELEANOR chooses LEFT.