Networked Anti-Coordination Games Meet Graphical Dynamical Systems: Equilibria and Convergence

TL;DR

This paper analyzes the existence and convergence of equilibria in networked anti-coordination games, revealing computational complexities and providing efficient solutions for special cases, with empirical validation on various networks.

Contribution

It introduces a novel analysis linking anti-coordination games to dynamical systems, identifying computational hardness and efficient cases, and studying convergence dynamics under different update schemes.

Findings

Finding an NE is efficient in the self non-essential mode but hard in the self essential mode.

Convergence occurs in polynomial steps for synchronous updates in both modes.

Sequential updates converge polynomially only in the self non-essential mode.

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.