The Max k-Cut Game and Its Strong Equilibria

An instance of the max k−cut game is an edge weighted graph. Every vertex is controlled by an autonomous agent with strategy space [1..k]. Given a player i, his payoff is defined as the total weight of the edges [i, j] such that player j’s strategy is different from player i’s strategy. The social welfare is defined as the weight of the cut, i.e. half the sum of the players payoff. It is known that this game always has a pure strategy Nash equilibrium, a state from which no single player can deviate. Instead we focus on strong equilibria, a robust refinement of the pure Nash equilibrium which is resilient to deviations by coalitions of any size. We study the strong equilibria of the max k−cut game under two perspectives: existence and worst case social welfare compared to a social optimum.