Asymmetric games on networks: Towards an Ising-model representation

A. D. Correia*, L. L. Leestmaker, H. T. C. Stoof, J. J. Broere

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

We here study the Battle of the Sexes game, a textbook case of asymmetric games, on small networks. Due to the conflicting preferences of the players, analytical approaches are scarce and most often update strategies are employed in numerical simulations of repeated games on networks until convergence is reached. As a result, correlations between the choices of the players emerge. Our approach is to study these correlations with a generalized Ising model. First, we show that these correlations emerge in simulations and can have an Ising-like form. Then, using the response strategy framework, we describe how the actions of the players can bring the network into a steady configuration, starting from an out-of-equilibrium one. We obtain these configurations using game-theoretic tools, and describe the results using Ising parameters. We exhaust the two-player case, giving a detailed account of all the equilibrium possibilities. Going to three players, we generalize the Ising model and compare the equilibrium solutions of three representative types of networks. We find that players that are not directly linked retain a degree of correlation that is proportional to their initial correlation. We also find that the local network structure is the most relevant for small values of the magnetic field and the interaction strength of the Ising model. Finally, we conclude that certain parameters of the equilibrium states are network independent, which opens up the possibility of an analytical description of asymmetric games played on networks. (C) 2022 The Author(s). Published by Elsevier B.V.
Original languageEnglish
Article number126972
Number of pages23
JournalPhysica A: Statistical Mechanics and its Applications
Volume593
Early online dateFeb 2022
DOIs
Publication statusPublished - 1 May 2022

Funding

We thank Kevin Peters for his early work on the introduction of correlations in the BoS game, Vincent Buskens for helpful discussions that improved our understanding of update strategies in simulations, and an anonymous referee for suggesting the discussion on potential games. This work is part of the D-ITP consortium, a program of the Netherlands Organization for Scientific Research (NWO) that is funded by the Dutch Ministry of Education, Culture and Science (OCW) . This work is also supported by the UU Complex Systems Fund, with special thanks to Peter Koeze.

FundersFunder number
Dutch Ministry of Education, Culture and Science (OCW)
UU Complex Systems Fund

    Keywords

    • Asymmetric games
    • Correlated games
    • Games on networks
    • Ising model

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