Jean Jacques Rousseau, presented the following situation: Two hunters can either jointly hunt a stag (an adult deer and rather large meal) or individually hunt a rabbit (tasty, but substantially less filling). Each hunter chooses between "stag" and "rabbit" without knowing the choice of the other hunter. Hunting stags is most beneficial for society, but it is quite challenging and requires mutual-cooperation: The hunters are able to hunt a stag only if both hunters choose to do so. If only one of the hunters chooses to hunt a stag, s/he fails. Each hunter can hunt a rabbit on their own, without any help. Each hunter prefers a larger meal, so they would most prefer to return home with a stag. Of course, a rabbit is still better than having no meal at all. a. [10 points] Write down the payoff matrix that represents this interaction. (Assign a payoff of "0" to the least preferred outcome, "1" to the next preferred one and so on.) b. [8 points] Find all pure strategy Nash Equilibria. Show your work clearly on the payoff matrix (best- response analysis). c. [4 points] For the Nash equilibria found in part (b), explain whether the equilibrium is Pareto Optimal. (If you found multiple Nash equilibria, answer this question for each equilibrium.) d. [3 points] Which class of games does the Stag Hunt Game belong to? (Consider the main classes of games discussed in class.) e. [5 points] Based on your answer to (d): ii. How do you interpret the fact that (R, R) is a Nash equilibrium of this game? What is the underlying social dilemma here? Discuss some ways of addressing this dilemma, and explain why you think they would work?