Convergence of best-response dynamics in games with conflicting congestion effects

We study the model of resource allocation games with conflicting congestion effects that was introduced by Feldman and Tamir [9]. In this model, an agent's cost consists of its resource's load (which increases with congestion) and its share in the resource's activation cost (which decreases with congestion). The current work studies the convergence rate of best-response dynamics (BRD) in the case of homogeneous agents. Even within this simple setting, interesting phenomena arise. We show that, in contrast to standard congestion games with identical jobs and resources, the convergence rate of BRD under conflicting congestion effects might be super-linear in the number of jobs. Nevertheless, a specific form of BRD is proposed, which is guaranteed to converge in linear time. •We analyze the convergence rate of best-response dynamics (BRD) in job scheduling games with homogeneous agents.•In games with either positive or negative congestion effect, BRD is known to converge to a Nash equilibrium in linear time.•We consider games in which positive and negative congestion effects occur simultaneously.•We show that the convergence rate of BRD in this case might be super-linear.•Yet, we propose a specific dynamic, referred to as max-cost BRD, where convergence occurs in linear time.