Computer Science > Computer Science and Game Theory
[Submitted on 7 Jan 2023 (v1), last revised 29 Mar 2024 (this version, v5)]
Title:Networked Anti-Coordination Games Meet Graphical Dynamical Systems: Equilibria and Convergence
View PDF HTML (experimental)Abstract:Evolutionary anti-coordination games on networks capture real-world strategic situations such as traffic routing and market competition. In such games, agents maximize their utility by choosing actions that differ from their neighbors' actions. Two important problems concerning evolutionary games are the existence of a pure Nash equilibrium (NE) and the convergence time of the dynamics. In this work, we study these two problems for anti-coordination games under sequential and synchronous update schemes. For each update scheme, we examine two decision modes based on whether an agent considers its own previous action (self essential ) or not (self non-essential ) in choosing its next action. Using a relationship between games and dynamical systems, we show that for both update schemes, finding an NE can be done efficiently under the self non-essential mode but is computationally intractable under the self essential mode. To cope with this hardness, we identify special cases for which an NE can be obtained efficiently. For convergence time, we show that the best-response dynamics converges in a polynomial number of steps in the synchronous scheme for both modes; for the sequential scheme, the convergence time is polynomial only under the self non-essential mode. Through experiments, we empirically examine the convergence time and the equilibria for both synthetic and real-world networks.
Submission history
From: Zirou Qiu [view email][v1] Sat, 7 Jan 2023 16:32:22 UTC (585 KB)
[v2] Fri, 3 Mar 2023 18:25:09 UTC (586 KB)
[v3] Fri, 8 Dec 2023 19:32:30 UTC (586 KB)
[v4] Sun, 18 Feb 2024 19:22:12 UTC (586 KB)
[v5] Fri, 29 Mar 2024 19:19:57 UTC (586 KB)
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