a) Must an Evolutionary Stable Strategy (ESS) be a Nash Equilibrium? Are all Nash equilibria ESSs?...

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a) Must an Evolutionary Stable Strategy (ESS) be a Nash Equilibrium? Are all Nash equilibria ESSs? b) For the Prisoners' Dilemma, Hawk-Dove, and Assurance Games, indicate which, if any, of the two strategies in each game are ESSs (assuming the only "mutant" strategy is the other one in the payoff matrix). c) Consider the following dove and hawk game where the prize(v) is 2 and the cost of fighting(c) is 10. Find the stable equilibrium(s). Hawk Hawk (v-c)/2, (v-c)/2 Dove v, 0 Dove 0, v v/2, v/2 d) In the Hawk-Dove game, is Hawk an ESS if the total prize in each fight is larger than Hawk's loss from fighting when faced with another Hawk (v>c)? Show your results mathematically. a) Must an Evolutionary Stable Strategy (ESS) be a Nash Equilibrium? Are all Nash equilibria ESSs? b) For the Prisoners' Dilemma, Hawk-Dove, and Assurance Games, indicate which, if any, of the two strategies in each game are ESSs (assuming the only "mutant" strategy is the other one in the payoff matrix). c) Consider the following dove and hawk game where the prize(v) is 2 and the cost of fighting(c) is 10. Find the stable equilibrium(s). Hawk Hawk (v-c)/2, (v-c)/2 Dove v, 0 Dove 0, v v/2, v/2 d) In the Hawk-Dove game, is Hawk an ESS if the total prize in each fight is larger than Hawk's loss from fighting when faced with another Hawk (v>c)? Show your results mathematically.