7 8 20 0 − 20 − 40 − 60 Empty Complete Bipartite Star NASH AND PAIRWISE NASH EQUILIBRIA α /γ β/γ 0 1 2 3 4 5 6 7 8 − 2 − 1 0 1 2 Empty Complete Bipartite Star Definition. The network is a Nash Equilibrium if • for all agents : 𝒢⋆ i Vi (ai , a−i ⋆ |θi) ≤ Vi (a⋆ i , a−i ⋆ |θi), ∀ai ∈ 𝒜 . Definition. The network is a Pairwise-Nash Equilibrium if •for all pairs of distinct agents : •for all pairs of distinct agents : 𝒢⋆ (i, j) Vi (aij , a⋆ i−(i, j) , a⋆ −i) ≤ Vi (a⋆ ij , a⋆ i−(i, j) , a⋆ −i), ∀aij ∈ [0,1], (i, j) Vi (aij , aji , a⋆ −(i, j)) > Vi (a⋆ ij , a⋆ ji , a⋆ −(i, j)) ⇓ Vj (aij , aji , a⋆ −(i, j)) < Vj (a⋆ ij , a⋆ ji , a⋆ −(i, j)) .