1. Describe with a neat sketch how the nanoparticles are prepared employing the top-down methods, namely, milling and lithography. 2. Explain with a suitable diagram, the synthesis of nanostructured materials….

## 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* (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 *υ*1(*s*) the fraction of individuals in the population who adopt the first action. Show that for any *ε*1*, ε*2 *> *0*,* there exists some ˆ*n*, *T** N such that the event {∀*t *≥ *T**, *|*υ*1(*s*(*t*)) − *ω*∗1 | ≤ *ε*1} has

probability no smaller than 1 − *ε*2 if the population size *n *≥ ˆ*n*.