Coalition Resilient Outcomes in Max k-Cut Games
Raffaello Carosi, Simone Fioravanti, Luciano Gual\`a, Gianpiero Monaco

TL;DR
This paper studies the existence and properties of strong Nash equilibria in max k-cut games, revealing cycles in coalition deviations, establishing existence of certain equilibria in unweighted graphs, and introducing local stability concepts.
Contribution
It demonstrates that minimal coalition deviations can cycle, shows optimal colorings are 5-strong equilibria in unweighted graphs, and introduces x-local strong equilibria with guaranteed existence.
Findings
Improving deviations by minimal coalitions can cycle.
Optimal colorings are 5-strong equilibria in unweighted graphs.
1-local strong equilibria always exist.
Abstract
We investigate strong Nash equilibria in the \emph{max -cut game}, where we are given an undirected edge-weighted graph together with a set of colors. Nodes represent players and edges capture their mutual interests. The strategy set of each player consists of the colors. When players select a color they induce a -coloring or simply a coloring. Given a coloring, the \emph{utility} (or \emph{payoff}) of a player is the sum of the weights of the edges incident to , such that the color chosen by is different from the one chosen by . 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. Very little is known about the existence of strong equilibria in max -cut games. In this paper we make some…
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Taxonomy
TopicsGame Theory and Applications · Game Theory and Voting Systems · Economic theories and models
