Consider a population consisting of two types, A and B, and assume that the change in...

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Consider a population consisting of two types, A and B, and assume that the change in the composition of the population is determined by the average payoffs received by the two types. A-types always play strategy A; B-types always play strategy B. Let x denote the share of A-types in the population. Assume that the players are matched randomly and receive payoffs described by the following payoff matrix: Player 1 A B Player 2 A B 0,0 k, 3 3, k 1,1 (a) Assuming that k = 2, i. derive the expected payoff to each of the two types of players as a function of the proportion (x) of players of type A. ii. analyze the evolution of the share of type A in the population. What is (are) the evolutionarily stable outcome(s) and the asso- ciated payoffs? (b) Now find a value of k such that A becomes a locally evolutionarily stable strategy. Explain why this value of k makes A an ESS. Consider a population consisting of two types, A and B, and assume that the change in the composition of the population is determined by the average payoffs received by the two types. A-types always play strategy A; B-types always play strategy B. Let x denote the share of A-types in the population. Assume that the players are matched randomly and receive payoffs described by the following payoff matrix: Player 1 A B Player 2 A B 0,0 k, 3 3, k 1,1 (a) Assuming that k = 2, i. derive the expected payoff to each of the two types of players as a function of the proportion (x) of players of type A. ii. analyze the evolution of the share of type A in the population. What is (are) the evolutionarily stable outcome(s) and the asso- ciated payoffs? (b) Now find a value of k such that A becomes a locally evolutionarily stable strategy. Explain why this value of k makes A an ESS.