Coalition Resilient Outcomes in Max k-Cut Games

We investigate strong Nash equilibria in the max k-cut game, where we are given an undirected edge-weighted graph together with a set \(\{1,\ldots , k\}\) of k colors. Nodes represent players and edges capture their mutual interests. The strategy set of each player v consists of the k colors. When players select a color they induce a k-coloring or simply a coloring. Given a coloring, the utility (or payoff) of a player u is the sum of the weights of the edges \(\{u,v\}\) incident to u, such that the color chosen by u is different from the one chosen by v. Such games form some of the basic payoff structures in game theory, model lots of real-world scenarios with selfish agents and extend or are related to several fundamental classes of games.

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