Problem 2 (7 pts) Two claimants are fighting in court over an asset that is worth $20,000. Assume that the likelihood of winning the case depends only on the number of hours of legal services the claimants purchase. In particular, assume that a claimant's probability of winning when purchasing n hours of legal services, while the other claimant purchases m hours, is n/(n+m). Claimants are billed x hundred dollars per hour of legal services. Thus claimants' (expected) payoffs are: n u(n, m) -200 - xn n+m m u2(n, m) - -200-xm n+m (counted in hundreds of dollars). a. Find the best response function of each claimant as a function of x. b. One can show that the Nash equilibrium of this game will be symmetric, that is, both claimants will choose the same number of hours at equilibrium. Assuming this (you don't need to prove it), compute the Nash equilibrium of the game as a function of x. c. Is the Nash equilibrium you just computed Pareto efficient? [Hint: find a pair of strategies that make both claimants better-off, even though they are not a NE.]