Optimalization Find p1, … , pn satisfying ∑ i∈N (ei − Ui(p ∗ )) ≤ 0 ei − Ui(s, p−i) ≥ 0 for each i ∈ N and every s ∈ Si pi ∈ ∆i for each i ∈ N ei ∈ R for each i ∈ N