Hedonic Diversity Games: A Complexity Picture with More than Two Colors

Ganian, Robert; Hamm, Thekla; Knop, Dušan; Schierreich, Šimon; Suchý, Ondřej

doi:10.1609/aaai.v36i5.20435

Cited by 7 publications

(4 citation statements)

References 19 publications

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“…Closest related to our model are Hedonic Diversity Games [Bredereck et al, 2019;Boehmer and Elkind, 2020;Darmann, 2021;Ganian et al, 2022], where agents of different types strategically form coalitions, and their utility depends on the fraction of same-type agents in their chosen coalition. While preferences over fractions may be arbitrary in these games, our model generalizes the special case with preferences resembling a τ -threshold function as in Schelling's model or with agents having single-peaked utilities with a peak at 1, since in our model the access to the resources can be restricted.…”

Section: Related Workmentioning

confidence: 99%

Strategic Resource Selection with Homophilic Agents

Harder

Krogmann

Lenzner

et al. 2023

Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence

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The strategic selection of resources by selfish agents is a classical research direction, with Resource Selection Games and Congestion Games as prominent examples. In these games, agents select available resources and their utility then depends on the number of agents using the same resources. This implies that there is no distinction between the agents, i.e., they are anonymous. We depart from this very general setting by proposing Resource Selection Games with heterogeneous agents that strive for a joint resource usage with similar agents. So, instead of the number of other users of a given resource, our model considers agents with different types and the decisive feature is the fraction of same-type agents among the users. More precisely, similarly to Schelling Games, there is a tolerance threshold tau in [0,1] which specifies the agents' desired minimum fraction of same-type agents on a resource. Agents strive to select resources where at least a tau-fraction of those resources' users have the same type as themselves. For tau=1, our model generalizes hedonic diversity games with single-peaked utilities with a peak at 1. For our general model, we consider the existence and quality of equilibria and the complexity of maximizing the social welfare. Additionally, we consider a bounded rationality model, where agents can only estimate the utility of a resource, since they only know the fraction of same-type agents on a given resource, but not the exact numbers. Thus, they cannot know the impact a strategy change would have on a target resource. Interestingly, we show that this type of bounded rationality yields favorable game-theoretic properties and specific equilibria closely approximate equilibria of the full knowledge setting.

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Section: Related Workmentioning

confidence: 99%

Strategic Resource Selection with Homophilic Agents

Harder

Krogmann

Lenzner

et al. 2023

Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence

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“…The central aim of such an endeavour is to identify the structural properties of the input-captured via numerical parameters-which give rise to fixed-parameter algorithms for the problem (see Section 2). Some examples where the parameterized complexity toolset has been successfully applied in the context of Artificial Intelligence research include the series of works on Hedonic Games (Boehmer and Elkind 2020a,b;Ganian et al 2022a), Integer Programming Eiben et al 2019;Dvorák et al 2021;Chan et al 2022), Data Completion (Ganian et al 2018Dahiya et al 2021;Ganian et al 2022b;Koana, Froese, and Niedermeier 2023), and Bayesian Network Learning (Ordyniak and Szeider 2013;Grüttemeier, Komusiewicz, and Morawietz 2021;Ganian and Korchemna 2021;Grüttemeier and Komusiewicz 2022).…”

Section: Introductionmentioning

confidence: 99%

The Complexity of Optimizing Atomic Congestion

Brand,

Ganian,

Kalyanasundaram

et al. 2024

AAAI

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Atomic congestion games are a classic topic in network design, routing, and algorithmic game theory, and are capable of modeling congestion and flow optimization tasks in various application areas. While both the price of anarchy for such games as well as the computational complexity of computing their Nash equilibria are by now well-understood, the computational complexity of computing a system-optimal set of strategies - that is, a centrally planned routing that minimizes the average cost of agents - is severely understudied in the literature. We close this gap by identifying the exact boundaries of tractability for the problem through the lens of the parameterized complexity paradigm. After showing that the problem remains highly intractable even on extremely simple networks, we obtain a set of results which demonstrate that the structural parameters which control the computational (in)tractability of the problem are not vertex-separator based in nature (such as, e.g., treewidth), but rather based on edge separators. We conclude by extending our analysis towards the (even more challenging) min-max variant of the problem.

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“…Also related are hedonic diversity games [Boehmer and Elkind, 2020, Bredereck et al, 2019, Ganian et al, 2022 where selfish agents form coalitions and the utility of an agent only depends on the type distribution of her coalition. For such games, single-peaked utility functions yield favorable game-theoretic properties.…”

Section: Introductionmentioning

confidence: 99%

Single-Peaked Jump Schelling Games

Friedrich¹,

Lenzner²,

Molitor³

et al. 2023

Preprint

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Schelling games model the wide-spread phenomenon of residential segregation in metropolitan areas from a game-theoretic point of view. In these games agents of different types each strategically select a node on a given graph that models the residential area to maximize their individual utility. The latter solely depends on the types of the agents on neighboring nodes and it has been a standard assumption to consider utility functions that are monotone in the number of same-type neighbors, i.e., more same-type neighbors yield higher utility. This simplifying assumption has recently been challenged since sociological poll results suggest that real-world agents actually favor diverse neighborhoods.We contribute to the recent endeavor of investigating residential segregation models with realistic agent behavior by studying Jump Schelling Games with agents having a single-peaked utility function. In such games, there are empty nodes in the graph and agents can strategically jump to such nodes to improve their utility. We investigate the existence of equilibria and show that they exist under specific conditions. Contrasting this, we prove that even on simple topologies like paths or rings such stable states are not guaranteed to exist. Regarding the game dynamics, we show that improving response cycles exist independently of the position of the peak in the utility function. Moreover, we show high almost tight bounds on the Price of Anarchy and the Price of Stability with respect to the recently proposed degree of integration, which counts the number of agents with a diverse neighborhood and which serves as a proxy for measuring the segregation strength. Last but not least, we show that computing a beneficial state with high integration is NP-complete and, as a novel conceptual contribution, we also show that it is NP-hard to decide if an equilibrium state can be found via improving response dynamics starting from a given initial state.

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Hedonic Diversity Games: A Complexity Picture with More than Two Colors

Cited by 7 publications

References 19 publications

Strategic Resource Selection with Homophilic Agents

Strategic Resource Selection with Homophilic Agents

The Complexity of Optimizing Atomic Congestion

Single-Peaked Jump Schelling Games

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