5. We can often think of terrorism as a war of attrition in which each time a side decides to fight, it imposes costs on the other. This is illustrated in the tree below. If A quits at the start of the game, it gets 0 and B gets the prize worth v. If A fights, it imposes cost on B who then decides whether to quit or fight. If B quits, A, who has yet to suffer any cost, gets v. B gets c. Looking down the tree, A is deciding at node [2m] whether to quit or fight. At this point, A has already fought m times and thus imposed total cost mc on B. Similarly, B has already fought m times and thus imposed cost mc on A. If A quits at [2m], its payoff is mec. If it fights, it imposes an additional cost c on B after which B decides to whether or not to quit. If B fights, it imposes and additional cost of on A and so on. The tree goes on forever, reflecting the idea that each side is always capable of fighting a little longer if it expects to prevail. Let py be the probability that the actor making the decision at node [k| fights. A 0] 0 ", A [2m] (=me,v me) A [2m+2] (v me,(m + 1)c) fyP2my2 (=(m+1)c,v (m+ 1)c) (a) What is the probability that A and B fight, i.e., what is pam, P2m+1, P2m+2, and, more generally, the probability of fighting at any node? [i.e., what is the mixed strategy equilibrium?] (b) What are A and B's equilibrium payoffs? () How much of the value of the prize v is dissipated through the war of attrition