Generalized Graph k-Coloring Games

Carosi, Raffaello; Monaco, Gianpiero

doi:10.1007/978-3-319-94776-1_23

Cited by 9 publications

(11 citation statements)

References 18 publications

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“…When it exists, an SE is a very robust state of the game and it is also more sustainable than an NE. However, while NE always exists in these games [8,15,18], little is known about the existence of strong equilibria in Max k-cut games. Indeed, to the best of our knowledge, there are basically two papers of the literature dealing with such issue.…”

Section: Introductionmentioning

confidence: 99%

“…In fact, for such a value of k, it coincides with the classical max cut game. In [8] the authors show the existence of NE in generalized max k-cut games where players also have an extra profit depending on the chosen color. When the graph is directed, the max k-cut game in general does not admit a potential function.…”

Section: Introductionmentioning

confidence: 99%

“…Studies on the performance of Nash equilibria and strong Nash equilibria can be found in [8,15,18] and in [11,12,13], respectively.…”

Section: Introductionmentioning

confidence: 99%

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Coalition Resilient Outcomes in Max k-Cut Games

Carosi

Fioravanti

Gualà

et al. 2019

Lecture Notes in Computer Science

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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, . . . , 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. Very little is known about the existence of strong equilibria in max k-cut games. In this paper we make some steps forward in the comprehension of it. We first show that improving deviations performed by minimal coalitions can cycle, and thus answering negatively the open problem proposed in [13]. Next, we turn our attention to unweighted graphs. We first show that any optimal coloring is a 5-SE in this case. Then, we introduce x-local strong equilibria, namely colorings that are resilient to deviations by coalitions such that the maximum distance between every pair of nodes in the coalition is at most x. We prove that 1-local strong equilibria always exist. Finally, we show the existence of strong Nash equilibria in several interesting specific scenarios.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Coalition Resilient Outcomes in Max k-Cut Games

Carosi

Fioravanti

Gualà

et al. 2019

Lecture Notes in Computer Science

Self Cite

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“…, c n /4 } contains both Ω(c 2 n ) edges and a perfect matching (if c n /4 is odd, we consider the first c n /4 + 1 nodes). 8 The first claim follows from standard arguments. Note that…”

Section: Corollary 3 (Sparse Random Coordination Games) Let D > 0 Bementioning

confidence: 99%

“…There is also a vast literature on different variants of anti-coordination (or cut) games, see, e.g., [16,18] and the references therein, which are also captured by our clustering games. In a recent paper, Carosi and Gianpiero [8] consider socalled k-coloring games. Moreover, clustering and coordination games were also studied on directed graphs [4,7].…”

Section: Convergence Of Best-response Dynamicsmentioning

confidence: 99%

Topological Price of Anarchy Bounds for Clustering Games on Networks

Kleer

Schäfer

2019

Web and Internet Economics

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We consider clustering games in which the players are embedded in a network and want to coordinate (or anti-coordinate) their choices with their neighbors. Recent studies show that even very basic variants of these games exhibit a large Price of Anarchy. Our main goal is to understand how structural properties of the network topology impact the inefficiency of these games. We derive topological bounds on the Price of Anarchy for different classes of clustering games. These topological bounds provide a more informative assessment of the inefficiency of these games than the corresponding (worst-case) Price of Anarchy bounds. As one of our main results, we derive (tight) bounds on the Price of Anarchy for clustering games on Erdős-Rényi random graphs, which, depending on the graph density, stand in stark contrast to the known Price of Anarchy bounds.

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