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.

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* (01) 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 Sdenote by υ1(s) the fraction of individuals in the population who adopt the first action. Show that for any ε1, ε0, there exists some ˆnT* N such that the event {∀≥ T|υ1(s(t)) − ω∗1 | ≤ ε1} has

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

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