In the Hawk-Dove game, two animals are fighting over some prey. Each can be passive or aggressive. Each prefers to be aggressive if its opponent is passive, and passive if its opponent is aggressive; given its own stance, it prefers the outcome when its opponent is passive to that in which its opponent is aggressive. (a) Formulate this situation as a strategic game and find its pure strategy Nash equilibria using best response correspondences. (You are free to create your own payoff function to represent the stated preferences.) (b) A variant of Hawk-Dove includes a third strategy - retaliate. The payoff table is shown below. Assume v> c> 0 and 0 < d < 0.5v. P1\P2 Agressive Passive 0.5v, 0.5v Retaliate 0.5(vc), 0.5(v-c) 0.5v +8,0.5v-8 Find all pure strategy Nash equilibria by using best response correspondences Agressive 0.5(v-c), 0.5(v -c) 0, v Passive v, 0 Retaliate 0.5(vc), 0.5(v-c) 0.5v8, 0.5v + 8 0.5v, 0.5v