A Unified Framework for Strong Price of Anarchy in Clustering Games

Feldman, Michal; Friedler, Ophir

doi:10.1007/978-3-662-47666-6_48

Cited by 13 publications

(23 citation statements)

References 17 publications

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“…subgraph density with respect to the graph G[E c ] (or simply G c ) induced by the coordination edges E c only is the crucial topological parameter determining the Price of Anarchy. These bounds provide more refined insights than the known (tight) bound of PoA ≤ c (number of colors) on the Price of Anarchy for (i) symmetric coordination games with individual preferences and arbitrary distribution rule [3], and (ii) clustering games without individual preferences and equal-split distribution rule [11] (both being special cases of our model). An important point to notice here is that this bound indicates that the Price of Anarchy is unbounded if the number of colors c = c(n) grows as a function of n. In contrast, our topological bounds are independent of c and are thus particularly useful when this number is large (while the maximum subgraph density is small).…”

Section: Topological Price Of Anarchy Boundmentioning

confidence: 97%

“…Prior to our work, the existence of pure Nash equilibria was known for certain special cases of coordination games only, namely for symmetric coordination games with individual preferences and c = 2 [3], and for symmetric coordination games without individual preferences [11]. To the best of our knowledge, this is the first characterization of distribution rules in terms of best-response dynamics (which, in particular, applies to the settings in which pure Nash equilibria are guaranteed to exist for every distribution rule [3,11]). 4 Related Work.…”

Section: Convergence Of Best-response Dynamicsmentioning

confidence: 99%

“…The literature on clustering and coordination games is vast; we only include references relevant to our model here. The proposed model above is a mixture of (special cases of) existing models in [3,4,11,21].…”

Section: Convergence Of Best-response Dynamicsmentioning

confidence: 99%

“…Different variants of clustering games have recently been studied intensively in the algorithmic game theory literature, both with respect to the existence and the inefficiency of equilibria (see, e.g., [3,4,11,15,16,18,20,21]). Unfortunately, several of these studies reveal that the strategic choices of the players may lead to equilibrium outcomes that are highly inefficient.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Topological Price Of Anarchy Boundmentioning

confidence: 97%

Section: Convergence Of Best-response Dynamicsmentioning

confidence: 99%

Section: Convergence Of Best-response Dynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Topological Price of Anarchy Bounds for Clustering Games on Networks

Kleer

Schäfer

2019

Web and Internet Economics

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“…For example, a tacit assumption is that if the payments provided are 'not enough', then every agent i can break off, and simultaneously generate a value of v(i) by working alone; such a solution does not make sense when the number of projects or possible coalitions is limited. Indeed, models featuring selfish agents choosing from a finite set of distinct strategies are the norm in many real-life phenomena: social or technological coordination [1,2], opinion formation [13,21], and party affiliation [6,8] to name a few.…”

Section: Introductionmentioning

confidence: 99%

Computing Stable Coalitions: Approximation Algorithms for Reward Sharing

Anshelevich

Sekar

2015

Web and Internet Economics

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Abstract. Consider a setting where selfish agents are to be assigned to coalitions or projects from a set P. Each project k ∈ P is characterized by a valuation function; v k (S) is the value generated by a set S of agents working on project k. We study the following classic problem in this setting: "how should the agents divide the value that they collectively create?". One traditional approach in cooperative game theory is to study core stability with the implicit assumption that there are infinite copies of one project, and agents can partition themselves into any number of coalitions. In contrast, we consider a model with a finite number of non-identical projects; this makes computing both high-welfare solutions and core payments highly non-trivial. The main contribution of this paper is a black-box mechanism that reduces the problem of computing a near-optimal core stable solution to the purely algorithmic problem of welfare maximization; we apply this to compute an approximately core stable solution that extracts one-fourth of the optimal social welfare for the class of subadditive valuations. We also show much stronger results for several popular sub-classes: anonymous, fractionally subadditive, and submodular valuations, as well as provide new approximation algorithms for welfare maximization with anonymous functions. Finally, we establish a connection between our setting and the well-studied simultaneous auctions with item bidding; we adapt our results to compute approximate pure Nash equilibria for these auctions.

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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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A Unified Framework for Strong Price of Anarchy in Clustering Games

Cited by 13 publications

References 17 publications

Topological Price of Anarchy Bounds for Clustering Games on Networks

Topological Price of Anarchy Bounds for Clustering Games on Networks

Computing Stable Coalitions: Approximation Algorithms for Reward Sharing

Coalition Resilient Outcomes in Max k-Cut Games

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