In a small Nevada town, Ptomaine Flats, there are only two restaurants, the Road Kill Café and, for Italian fare, Sal Monella's. Each restaurant has to decide whether to clean up its act or continue to ignore health code violations.
Each restaurant currently makes $\$ 7,000$ a year in profit. If they both tidy up a bit, they will attract more patrons but must bear the (substantial) cost of the cleanup; so they will both be left with a profit of $\$ 5,000 .$ However, if one cleans up and the other doesn't, the influx of diners to the cleaner joint will more than cover the costs of the scrubbing; the more hygienic place ends up with $\$ 12,000,$ and the grubbier establishment incurs a loss of $\$ 3,000$
a. Write out the payoff matrix for this game, clearly labeling strategies and payoffs to each player.
b. What is each player's dominant strategy?
c. What will be the outcome of the game? Explain your answer.
d. Suppose the two restaurants believe they will face the same decision repeatedly. How might the outcome differ? Why?
e. Assume that if one cleans up and one stays dirty, the cleaner restaurant makes only $\$ 6,000$ in profit. All other payoffs are the same as before. What will the outcome of the game be now without cooperation? With cooperation?