After a lot of market research, you decide that Upstate New York does not have enough toy stores, so you are thinking about opening up a small toy shop. Unfortunately, Toys R Us, a very large and well-known toy store, is also thinking about opening up a new store that would directly compete with yours. Both of you are trying to decide whether to open up a shop in Saratoga Springs or in Utica. Each firm will only set up one shop (not one in each).
a) Create hypothetical expected profits for both you and for Toys R Us based on where the two of you set up shop. There are many right answers, but I want the payoffs you create to have two features. First, Toys R Us is a much bigger store and it should get much larger profits in all scenarios than you do. Second, no player should have a dominant strategy. Explain your choices.
b) Suppose that you and Toys R Us must make your decisions simultaneously. Given the payoffs you created above, find all equilibria in pure and mixed strategies for the game. What are the expected profits for each company in those equilibria?
c) If this was the real world, what strategic moves might you make to try to get a better payoff? Use at least one of the following terms (commitment, contract, credibility device, deterrence, reputation, response rule, promise, or threat) in your answer.