1. (35 points) In a small Nevada town, Ptomaine Flats, there are only two restaurants: the Road Kill Cafe and, for Italian fare, Sal Monella's. Each restaurant has to decide whether to clean up its act or to continue health code violations. If they both clean up they will attract more customers, but must bear the (substantial) cost of the cleanup. However, if one cleans up and the other does not, the influx of diners to the cleaner restaurant will more than cover the cost of the scrubbing. This is captured in the following strategic-form game. RKC\SM Clean up Don't Clean up 12,5 16,1 Don't 5,12 14,10 a) Find the Nash equilibrium (there is only one). b) Find the cooperative outcome. Explain why this is not strategically stable. Now, suppose that instead of interacting only once, Road Kill Caf and Sal Monella's share the market indefinitely. After each period, both firms can tell what occurred in the game in the previous period. Each one discounts the future using a discount factor denoted by RKC and SSM for Road Kill Caf and Sal Monella's, respectively. Moreover, suppose that both firms use the grim-trigger strategy of cooperating as long as their competitor has cooperated, and playing the Nash equilibrium strategy forever if it has not. c) What is the smallest value of 5c that makes cooperation in every period an equilibrium choice for Road Kill Cafe if Sal Monella's does not cheat? You must prove your answer. d) What is the smallest value of that makes cooperation in every period an equilibrium choice for Sal Monella's if Road Kill Caf does not cheat? You must prove your answer. e) Explain any difference in your answer to parts c) and d).