A war of attrition game.) Two small grocery stores on the same block are feeling the effects of a large supermarket that was recently constructed a half-mile away.

As long as both remain in business, each will lose $1000 per month. On the first day of every month, when the monthly rent for the stores is due, each grocer who is still in business must independently decide whether to stay in business for another month or to quit. If one grocer quits, then the grocer who remains will make $500 per month profit thereafter.

Assume that, once a grocer quits, his or her lease will be taken by some other merchant (not a grocer), so he or she will not be able to reopen a grocery store in this block, even if the other grocer also quits. Each grocer wants to maximize the expected discounted average value of his or her monthly profits, using a discount factor per month of δ = .99.

a. Find an equilibrium of this situation in which both grocers randomize between staying and quitting every month until at least one grocer quits.

b. Discuss another way that the grocers might handle this situation, with reference to other equilibria of this game.

c. Suppose now that grocer 1 has a slightly larger store than grocer 2. As long as both stores remain in business, grocer 1 loses $1200 per month and grocer 2 loses $900 per month. If grocer 1 had the only grocery store on the block, he would earn $700 profit per month.

If grocer 2 had the only grocery store on the block, she would earn $400 per month.

Find an equilibrium of this situation in which both grocers randomize between staying and quitting every month, until somebody actually quits. In this equilibrium, which grocer is more likely to quit first?