2. Resolving conflicts by flipping a fair coin (10 points). Consider a game of potential conflict between two players for a prize valued at v by both takes place in two sequential stages, the conflict resolution stage and the conflict stage. stage, players 1 and 2 simultaneously decide whether to resolve the conflict by flipping strategy "Flip") or to enter the conflict stage (call this strategy "Conflict"). If both playe the game ends with neither player advancing to the conflict stage. The prize is allocated probability pit ? = p1 = 0.5, and players 1 and 2 receive the expected payoffs of E(m However, if either player refuses to "Flip" (i.e., one or both players choose "Conflict"). advance to the conflict stage. In the conflict stage, both players make irreversible effort e2 2: 0 to increase their probabilities of receiving the prize. Players have different conflict 0 and a2 > 0, so that the stronger player 1 (a1 > a2) can expend the same effort, yet winning the prize. Specifically, player 1's probability of winning is pi(el, e2) = ciel/(are probability of winning is pi(e1,e2) = azer/(aren + azez). The expected payoff in a conflict E(m Conflict) = pi(e1,ez)v - e1 = vanier/(are + azez) - el and the expected payoff in a conflid E(my Conflict) = pr(e1, en)v - en = vanner (chel + azez) - ex. a) What is the Nash equilibrium of the conflict stage subgame? (2 points). Hint: In the c players will maximize their respective payoffs, so just solve the following two First Ord BE(m] Conflict)/de1 = 0 and E(my Conflict)/dez = 0 simultaneously, in order to get el* and en . b) What is the Nash equilibrium payoff in the conflict stage? (2 points). Hint: Plug in th into E(m Conflict) and E(my Conflict) to get the Nash equilibrium payoffs