A. Consider a round-robin context where the underlying bilateral

game is a coordination game (cf. (11.20) and (11.21)). Show that all pure-strategy

Nash equilibria are mono morphic.

B. Consider a round-robin context where the underlying bilateral game involves only two actions and displays a unique symmetric equilibrium,which is in completely mixed strategies. Let ω

*1* (0, 1) stand for the weight associated with the first action by the (common) mixed strategy played in this equilibrium. On the other hand, given any strategy profile s * S, denote by υ1(s) the fraction of individuals in the population who adopt the first action. Show that for any ε1, ε2 > 0, there exists some ˆn, T* N such that the event {∀t ≥ T, |υ1(s(t)) − ω∗1 | ≤ ε1} has

probability no smaller than 1 − ε2 if the population size n ≥ ˆn.