PLEASE PROVIDE FULL SOLUTION SO THAT I CAN LEARN TO DO SIMILAR PROBLEMS The Hung

Question

PLEASE PROVIDE FULL SOLUTION SO THAT I CAN LEARN TO DO SIMILAR PROBLEMS

The Hunger Games Two players, Katnis and Peeta, are playing the Hunger Games. Each player has two strategies they must choose from: to cooperate with each other, or, to defect and play the game alone. The payoffmatrix is given below. Peeta's payoffs are given in the upper right triangle of each square and Katnis' payoffs are given in the lower right triangle of each square. Does Peeta have a dominant strategy, and if so, what is it? Does Katnis have a dominant strategy, and if so, what is it? Is there a Nash equilibrium to this game, and if so, what is it?

Explanation / Answer

Peeta has a dominant strategy i.e Cooperate as

comparing the 2 columns - 3>0, 1>0

Katnis doesn't have a dominant strategy as

by comparing the two rows, there is not a single row that has higher payoffs for alll the possibilities

There exists a Nash quilibrium at (3,3) i.e when Peeta and Katni cooperate as none of them will get a higher payoff vy defecting from the strategies.

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