Distance Hedonic Games

Flammini, Michele; Kodric, Bojana; Olsen, M. W.; Varricchio, Giovanna

doi:10.1007/978-3-030-67731-2_12

Cited by 3 publications

(2 citation statements)

References 18 publications

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“…Like in hedonic games, there is no topology graph in social distance games. Flammini et al (2021) introduced distance hedonic games, which generalize social distance games by allowing the distance function to be arbitrary rather than specifically the reciprocal function. Rey and Rey (2022) considered a distance-based approach for extending the agents' preferences over neighbors to preferences over coalitions in a subclass of hedonic games.…”

Section: Related Workmentioning

confidence: 99%

Topological Distance Games

Bullinger

Suksompong

2023

AAAI

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We introduce a class of strategic games in which agents are assigned to nodes of a topology graph and the utility of an agent depends on both the agent's inherent utilities for other agents as well as her distance from these agents on the topology graph. This model of topological distance games (TDGs) offers an appealing combination of important aspects of several prominent settings in coalition formation, including (additively separable) hedonic games, social distance games, and Schelling games. We study the existence and complexity of stable outcomes in TDGs—for instance, while a jump stable assignment may not exist in general, we show that the existence is guaranteed in several special cases. We also investigate the dynamics induced by performing beneficial jumps.

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Section: Related Workmentioning

confidence: 99%

Topological Distance Games

Bullinger

Suksompong

2023

AAAI

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“…To capture the utility of an agent v in a coalition C ⊆ V , the model considered a single function: (v,w) where d C (v, w) is the distance between v and w inside C. Social distance games with the aforementioned utility function u have been the focus of extensive study to date, with a number of research papers specifically targeting algorithmic and complexitytheoretic aspects of forming coalitions with maximum social welfare [1,2,3,28]. Very recently, Flammini et al [21,22] considered a generalization of u via an adaptive real-valued scoring vector which weights the contributions to an agent's utility according to the distances of other agents in the coalition, and studied the price of anarchy and stability for non-negative scoring vectors. However, research to date has not revealed any polynomially tractable fragments for the problem of computing coalition structures Figure 1: A social network illustrating the difference of maximising social welfare in our model compared to previous SDG models.…”

Section: Introductionmentioning

confidence: 99%

Maximizing Social Welfare in Score-Based Social Distance Games

Ganian¹,

Hamm²,

Knop³

et al. 2023

Electron. Proc. Theor. Comput. Sci.

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Social distance games have been extensively studied as a coalition formation model where the utilities of agents in each coalition were captured using a utility function u that took into account distances in a given social network. In this paper, we consider a non-normalized score-based definition of social distance games where the utility function u s depends on a generic scoring vector s, which may be customized to match the specifics of each individual application scenario.As our main technical contribution, we establish the tractability of computing a welfare-maximizing partitioning of the agents into coalitions on tree-like networks, for every score-based function u s . We provide more efficient algorithms when dealing with specific choices of u s or simpler networks, and also extend all of these results to computing coalitions that are Nash stable or individually rational. We view these results as a further strong indication of the usefulness of the proposed score-based utility function: even on very simple networks, the problem of computing a welfare-maximizing partitioning into coalitions remains open for the originally considered canonical function u.

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Distance Polymatrix Coordination Games

Aloisio

Flammini

Kodric

et al. 2021

Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence

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In polymatrix coordination games, each player x is a node of a graph and must select an action in her strategy set. Nodes are playing separate bimatrix games with their neighbors in the graph. Namely, the utility of x is given by the preference she has for her action plus, for each neighbor y, a payoff which strictly depends on the mutual actions played by x and y. We propose the new class of distance polymatrix coordination games, properly generalizing polymatrix coordination games, in which the overall utility of player x further depends on the payoffs arising by mutual actions of players v,z that are the endpoints of edges at any distance h<d from x, for a fixed threshold value d≤n. In particular, the overall utility of player x is the sum of all the above payoffs, where each payoff is proportionally discounted by a factor depending on the distance h of the corresponding edge. Under the above framework, which is a natural generalization that is well-suited for capturing positive community interactions, we study the social inefficiency of equilibria resorting to standard measures of Price of Anarchy and Price of Stability. Namely, we provide suitable upper and lower bounds for the aforementioned quantities, both for bounded-degree and general graphs.

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Distance Hedonic Games

Cited by 3 publications

References 18 publications

Topological Distance Games

Topological Distance Games

Maximizing Social Welfare in Score-Based Social Distance Games

Distance Polymatrix Coordination Games

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