6. A village's two villagers hold as common property a local forest from which they harvest nuts. If a villager exercises restraint, he exerts a quantity of labor equivalent to 5 in cost. If he does not exercise restraint, he exerts a quantity of labor equivalent to 10 in cost. If both exercise restraint, they each obtain a harvest worth 15. If neither exercises restraint they each obtain a harvest worth 18. If one exercises restraint and the other does not, the one who exercises restraint obtains revenue of 9, and the one who does not obtains revenue of 22. a. Fill in the following table to describe the payoffs in this game. Villager 2 No restraint Restraint Restraint Villager 1 No restraint b. Suppose an external authority imposes a rule requiring each Villager to exercise restraint. Any villager caught harvesting in an unrestrained fashion must pay a fine F. At least how high must Fbe to make restrained use the dominant strategy for both players? At least how high must F be to create the potential for a good equilibrium in which both exercise restraint (but not necessarily guarantee the good equilibrium)? c. Now suppose that the external authority is able to detect unrestrained use with probability of only 0.5. Suppose further that each villager maximizes expected profits. This means that the payoff he obtains when facing a probability p of paying a fine Fis equal to R-L-pF, where R is his revenue and Lis his labor cost. At least how high must F be to create the potential for a good equilibrium in which both exercise restraint