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Generalized Distance Polymatrix Games

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SOFSEM 2024: Theory and Practice of Computer Science (SOFSEM 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14519))

Abstract

We consider a generalization of the distance polymatrix coordination games to hypergraphs. The classic polymatrix coordination games and the successive distance polymatrix coordination games are usually modelled by means of undirected graphs, where nodes represent agents, and edges stand for binary games played by the agents at their extremes. The utility of an agent depends at different scales on the outcome of a suitably defined subset of all binary games, plus the preference she has for her action.

We propose the new class of generalized distance polymatrix games, properly generalizing distance polymatrix coordination games, in which each subgame can be played by more than two agents. They can be suitably modelled by means of hypergraphs, where each hyperedge represents a subgame played by its agents. Moreover, as for distance polymatrix coordination games, the overall utility of a player x also depends on the payoffs of the subgames where the involved players are far, at most, a given distance from x. As for the original model, we discount these payoffs proportionally by factors depending on the distance of the related hyperedges.

After formalizing and motivating our model, we first investigate the existence of exact and approximate strong equilibria. Then we study the degradation of the social welfare by resorting to the standard measures of Price of Anarchy and Price of Stability, both for general and bounded-degree graphs.

This work is partially supported by GNCS-INdAM and European Union, PON Ricerca e Innovazione 2014-20 TEBAKA - Fondo Sociale Europeo 2014-20.

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Notes

  1. 1.

    A hypergraph \(\mathcal {H}\) has degree bounded by \(\varDelta \) if the degree of every node x of \(\mathcal {H}\) is at most \(\varDelta \).

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Author information

Authors and Affiliations

  1. Universitá degli Studi Internazionali di Roma, Rome, Italy

    Alessandro Aloisio

  2. Gran Sasso Science Institute, L’Aquila, Italy

    Michele Flammini

  3. Universitá del Salento, Lecce, Italy

    Cosimo Vinci

Authors
  1. Alessandro Aloisio
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  2. Michele Flammini
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  3. Cosimo Vinci
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Corresponding author

Correspondence to Alessandro Aloisio .

Editor information

Editors and Affiliations

  1. University of Trier, Trier, Germany

    Henning Fernau

  2. UNSW Sydney, Sydney, NSW, Australia

    Serge Gaspers

  3. CNRS and University of Bordeaux, Talence, France

    Ralf Klasing

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Aloisio, A., Flammini, M., Vinci, C. (2024). Generalized Distance Polymatrix Games. In: Fernau, H., Gaspers, S., Klasing, R. (eds) SOFSEM 2024: Theory and Practice of Computer Science. SOFSEM 2024. Lecture Notes in Computer Science, vol 14519. Springer, Cham. https://doi.org/10.1007/978-3-031-52113-3_2

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  • DOI: https://doi.org/10.1007/978-3-031-52113-3_2

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  • Print ISBN: 978-3-031-52112-6

  • Online ISBN: 978-3-031-52113-3

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