Generalize the evolutionary approach introduced at the beginning of Section 12.4 as follows. Suppose each player i*N mutates with respective (idiosyncratic) probabilities εi , which are determined by corresponding smooth functions φi : [0, 1) → [0, 1), εi = φi (ε), where ε is the common base parameter reflecting the “overall level of noise” in the system. Further suppose that φi (0) = 0 and

 

It can be shown that the techniques presented in Section 12.6 can be used to obtain

the same results as in the text for each of the different strategic setups considered.

Prove it in detail for the case in which the population plays a bilateral coordination

game under global interaction.