Equilibria and learning dynamics in mixed network coordination/anti-coordination games

TL;DR

This paper investigates the existence and convergence of pure-strategy Nash equilibria in complex mixed network games with both coordinating and anti-coordinating players, providing graph-theoretic conditions and dynamic analysis.

Contribution

It introduces graph-theoretic conditions for equilibrium existence and analyzes the convergence of best-response dynamics in mixed network games.

Findings

Graph-theoretic conditions for pure-strategy Nash equilibria

Sufficient conditions for finite-time convergence of dynamics

Extension of network cohesiveness and new concept of network indecomposability

Abstract

Whilst network coordination games and network anti-coordination games have received a considerable amount of attention in the literature, network games with coexisting coordinating and anti-coordinating players are known to exhibit more complex behaviors. In fact, depending on the network structure, such games may even fail to have pure-strategy Nash equilibria. An example is represented by the well-known matching pennies (discoordination) game. In this work, we first provide graph-theoretic conditions for the existence of pure-strategy Nash equilibria in mixed network coordination/anti-coordination games of arbitrary size. For the case where such conditions are met, we then study the asymptotic behavior of best-response dynamics and provide sufficient conditions for finite-time convergence to the set of Nash equilibria. Our results build on an extension and refinement of the notion of network cohesiveness and on the formulation of the new concept of network indecomposibility.