4. Clever Mutants. (20 points) Consider the symmetric two-player game: 0 3 0 0 (

Question

4. Clever Mutants. (20 points) Consider the symmetric two-player game: 0 3 0 0 (a) (10 points) Find all the evolutionarily stable strategies, including any mixed- strategy (i.e., polymorphic) ESS. Explain your answer. (b) (10 points) Now, suppose that mutants have a 'secret handshake'. That is, suppose that mutants can recognize other mutants and play different pure strategies against normal and mutant opponents. For example, a mutant could play b against another mutant but play a against a non-mutant. Argue informally there can no longer be an ESS in which only b is played

Explanation / Answer

Answer:

(a)

An evolutionarily stable strategy is a strategy which could not be evaded by other strategies. Nash Equilibrium reflects no gain to deviate from the initial strategy without a change in the strategy of others. In the given symmetric two-player game: payoff matrix, there are three Nash Equilibria which are (a, a), (b, b), and [(1/4,3/4), (1/4,3/4)] because these cannot be improved by changing initial strategy except change of strategies by others. However, there are two evolutionarily stable strategies which are (a, a) and (b, b) because these cannot be could not evade the population of b and b also could not invade the population of b.

(b)

It is assumed that initial Nash equilibrium is at (b, b) because they would always play ‘a’ against mutants but non-mutants would not recognize mutants adopted strategies. In case the mutants take entry in to the population by recognizing their own strategies via ‘secrete handshake’ so they can easily play ‘a’ strategy against mutants and play ‘b’ strategy against non-mutants. In this manner, the mutants would get 3 every time with other mutants whereas the mutants get 1 every time with non-mutants. Therefore, it can be seen that the mutants’ strategies are best responsive to the normal’s strategies, but it provides better response to itself in comparison to the normal’s strategies response. It would fail the normal strategies to be evolutionarily stable strategies.

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.