[The Free Rider Problem] Mike and Chip go to a restaurant. For simplicity, assume that the restaurant serves only two types of meals: the 3 course meal (3M) that costs $22, and the sandwich combo (SC) which costs $10. Assume that for both Mike and Chip the 3 course meal (3M) is worth $20, while the sandwich combo (SC) is worth $10.

a. If Mike and Chip agree that each of them will pay his own check, what would each individual order? Hint: compute the consumer surplus of buying 3M and that of SC for each individual, they would order what maximizes their surplus.

Now assume that before ordering anything, Mike and Chip agree to split the bill between the two. Now we will determine what each individual would order (assuming that they only care about their surplus). There are 4 possible outcomes in this problem.

1) Both order SC (and split the check)

2) Mike orders SC and Chip orders 3M (and split the check)

3) Mike orders 3M and Chip orders SC (and split the check)

4) Both order 3M (and split the check)

For each possible outcome, we determine the surplus of each individual. For example, if both order SC the total cost would be $20, and so each one would pay $10. Since each values that meal at $10, their surplus is 0. However, if Mike orders SC and Chip orders 3M, each would pay $16 (the splitted check) and hence Mike would have a negative surplus (-6), and Chip woud have a positive surplus (+6).

Assume that individuals care only about their own surplus, and that they order exactly at the same time.

b. Write down this game in normal form (the bimatrix) and then solve for the Nash Equilibria

c. Explain why the outcome is dierent than if each individual pays its own check.

d. The structure of this game has many applications. For example, you could think of sustainable fishing. (SC = sustainable fishing where all fishermen in a town agree to a certain quota of fish, 3M=fishing more than the agreed quota). What are the individual incentives of the fishermen?