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- W2400484639 abstract "Various social networks, and some computational problems, require forming groups in the presence of de facto antagonistic relationships denoting local incompatibility. This can be posed as a vertex graph coloring problem, and the configurations attainable under these constraints through coordinated algorithms (e.g., aiming at using the least amount of colors) are well characterized. In contrast, when groups are formed in a distributed manner by self-interested nodes, we know surprisingly little of the configurations that emerge from the dynamics of such a coloring game. Collusions – multiple players joining a new group together so that they all improve their scores – are likely to occur in such group formation settings; they greatly affect the stability and efficiency of the configurations. This paper characterizes the convergence of coloring games, revealing their intricate complexity properties and proving that previous bounds are arbitrarily loose. First, in a uniform game, we show that sequences of moves relate to physics models of condensed matter and integer partition. Moreover, we prove that combinatorial complexity of coloring games suddenly increases: no polynomial bound exists whenever this analysis fails. This solves an open problem and explains the failure of previous proposed methods using potential functions. In non-uniform games where nodes preferences are given in a set of weights, we prove generally the maximum collusion size that guarantees convergence. As we show, deciding the convergence beyond this point is never computationally feasible. Our results extend to variants where nodes join multiple groups, have asymmetrical weights, and utility goes beyond pairwise relationship. Finally, we show these games create a tension between stability and efficiency, as collusions and using multiple colors both have a beneficial effect on the price of anarchy." @default.
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- W2400484639 date "2012-12-16" @default.
- W2400484639 modified "2023-09-27" @default.
- W2400484639 title "Convergence of Coloring Games with Collusions" @default.
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