4.4 You and a competitor own two stores in the same town that sell musical instruments. The two of you can either set high prices or set low prices. You know your profits but can only estimate your rival’s profits. If you both set high prices, your economic profit will be $4 million, and you think your rival will make a large profit. If you both set low prices, your economic profit will be zero, and you think your rival also will make no economic profit. If you set high prices and your rival sets low prices, you will have an economic loss of $2 million, and you forecast that your rival will have a very large profit. Finally, if you set low prices and your rival sets high prices, you will have a profit of

$5 million, and you believe your rival will have an economic loss.

a. What is the payoff matrix for this game?

b. If the game is played only once, do you have a dominant strategy? If so, what is it? Does your rival have a dominant strategy? If so, what is it? What is the Nash equilibrium of the game?

c. If the game is played repeatedly, what is the cooperative equilibrium? What strategy (or strategies) could you adopt?