Partition Equilibrium Always Exists in Resource Selection Games

Anshelevich, Elliot; Caskurlu, Bugra; Hate, Ameya

doi:10.1007/978-3-642-16170-4_5

Cited by 5 publications

(23 citation statements)

References 13 publications

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“…Also, in singleton congestion games an outcome that satisfies axiom A1 always exists, since it is a subclass of congestion games, for which the existence of a Nash equilibrium is guaranteed [11]. In RSGs with increasing cost functions, there always exists an outcome that satisfies axioms A1 and A3 [1]. 3 However, as mentioned earlier, there does not always exist an outcome that also satisfies axiom A2 [4].…”

Section: Related Workmentioning

confidence: 94%

On Singleton Congestion Games with Resilience Against Collusion

Caskurlu¹,

Ekici²,

Kizilkaya³

2020

Preprint

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We study the subclass of singleton congestion games with identical and increasing cost functions, i.e., each agent tries to utilize from the least crowded resource in her accessible subset of resources. Our main contribution is a novel approach for proving the existence of equilibrium outcomes that are resilient to weakly improving deviations: (i) by singletons (Nash equilibria), (ii) by the grand coalition (Pareto efficiency), and (iii) by coalitions with respect to an a priori given partition coalition structure (partition equilibria). To the best of our knowledge, this is the strongest existence guarantee in the literature of congestion games that is resilient to weakly improving deviations by coalitions.

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Section: Related Workmentioning

confidence: 94%

On Singleton Congestion Games with Resilience Against Collusion

Caskurlu¹,

Ekici²,

Kizilkaya³

2020

Preprint

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“…For studies on the computation of a Nash equilibrium, see Caragiannis et al (2011), Chien andSinclair (2011), andHarks andTimmermans (2017). For other studies on congestion games and its special instances, see Feldman and Tennenholtz (2010), Anshelevich et al (2013), and Caskurlu et al (2020a, 2020b, 2021.…”

Section: Related Literaturementioning

confidence: 99%

Location Choice under Spillovers

Ekici¹,

Caskurlu²

2022

berj

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This paper introduces the location choice under spillovers game: A number of firms choose from among a number of alternative locations. A firm's payoff at some location is the sum of two factors: Its location-specific idiosyncratic payoff; and the positive spillover it receives, which is a function of the number of firms choosing the same location. The spillover function is location-specific and monotonically increasing. This game form can be viewed as an extension of the classic "battle of sexes" game. It can also be used to model real-life game-theoretic situations with network effects, such as when app users choose from alternative social media or instant messaging apps. In our main result, we show that the location choice under spillovers game is a potential game, and hence, it always admits a Nash equilibrium in pure strategies. We also show that: A Nash equilibrium outcome need not be Pareto efficient. An outcome that is Pareto efficient need not be a Nash equilibrium. And a Nash equilibrium is not necessarily a strong equilibrium.

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“…Our results in RSGs and their relation to the results in the literature are as follows: Feldman and Tennenholtz [5] showed that a partition equilibrium always exists in RSGs under the following restrictions: (i) if the size of a viable coalition is bounded by 2; or (ii) if there are only two resources; or (iii) if the resources are identical. Anshelevich et al [1] generalized this result by proving a strategy profile that is both a partition equilibrium and a Nash equilibrium is guaranteed to exist in general RSGs. Our findings are as follows:…”

Section: Introductionmentioning

confidence: 98%

“…First of all, a super strong equilibrium rarely exists in a game. Therefore, restrictions on coalition formation may be helpful to obtain existence results 1 . This is the very same idea behind the well-known Nash equilibrium [16] solution concept where only singletons are viable coalitions.…”

Section: Introductionmentioning

confidence: 99%

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On Existence of Equilibrium Under Social Coalition Structures

Caskurlu¹,

Ekici²,

Kizilkaya³

2019

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In a strategic form game a strategy profile is an equilibrium if no viable coalition of agents (or players) benefits (in the Pareto sense) from jointly changing their strategies. Weaker or stronger equilibrium notions can be defined by considering various restrictions on coalition formation. In a Nash equilibrium, for instance, the assumption is that viable coalitions are singletons, and in a super strong equilibrium, every coalition is viable. Restrictions on coalition formation can be justified by communication limitations, coordination problems or institutional constraints. In this paper, inspired by social structures in various real-life scenarios, we introduce certain restrictions on coalition formation, and on their basis we introduce a number of equilibrium notions. As an application we study our equilibrium notions in resource selection games (RSGs), and we present a complete set of existence and non-existence results for general RSGs and their important special cases.

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Partition Equilibrium Always Exists in Resource Selection Games

Cited by 5 publications

References 13 publications

On Singleton Congestion Games with Resilience Against Collusion

On Singleton Congestion Games with Resilience Against Collusion

Location Choice under Spillovers

On Existence of Equilibrium Under Social Coalition Structures

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