Independent Lazy Better-Response Dynamics on Network Games

TL;DR

This paper analyzes a new independent lazy better-response dynamic in network games, providing bounds on convergence time based on network degree, revision probability, and game potential, suitable for distributed systems.

Contribution

It introduces and studies an independent, probabilistic best-response dynamic, extending classical models to better suit distributed environments.

Findings

Derived bounds on convergence time for the proposed dynamics.

Showed the dynamics' suitability for distributed systems.

Compared the new dynamics with classical sequential models.

Abstract

We study an independent best-response dynamics on network games in which the nodes (players) decide to revise their strategies independently with some probability. We provide several bounds on the convergence time to an equilibrium as a function of this probability, the degree of the network, and the potential of the underlying games. These dynamics are somewhat more suitable for distributed environments than the classical better- and best-response dynamics where players revise their strategies "sequentially", i.e., no two players revise their strategies simultaneously.