(i) In a spirit similar to that of Exercise 12.9, now assume that the mutation

probabilities may depend on the prevailing state so that there is some

smooth function φ : [01) × → [01)where εω φ(ε, ω) is the mutation

probability at state ω when the base parameter reflecting the overall

noise of the system is ε. (For simplicity, assume all players mutate with the

same probability.) Further suppose that φ(0·) = 0 and, as the counterpart

of (12.62), we have that for each ω,ω

_ *_. Focus on the context in which the population plays

a bilateral coordination game under global interaction and show that the

results established in the text are not affected by the proposed variation.

(ii) Now consider a situation such as the one described in (i) above but, instead

of (12.63), suppose φ(ε, ω) = ε for all ω _= ωα but for some * NGiven (the population size), characterize the values of

that lead to the same selection result (i.e., the same stochastically stable

state) as in the text. What happens for other values of r?