Binary Log-Linear Learning with Stochastic Communication Links

TL;DR

This paper extends binary log-linear learning in multi-agent systems to account for stochastic communication links, deriving conditions for desired equilibrium probabilities and demonstrating a transition phenomenon.

Contribution

It introduces a framework for analyzing potential games with stochastic communication, expanding beyond ideal links to include probabilistic connectivity conditions.

Findings

Derived conditions on link connectivity probability for desired equilibrium distribution

Identified a transition phenomenon in potential maximizer probabilities

Extended existing binary log-linear learning models to stochastic communication scenarios

Abstract

In this paper, we consider distributed decision-making over stochastic communication links in multi-agent systems. We show how to extend the current literature on potential games with binary log-linear learning (which mainly focuses on ideal communication links) to consider the impact of stochastic communication channels. More specifically, we derive conditions on the probability of link connectivity to achieve a target probability for the set of potential maximizers (in the stationary distribution). Furthermore, our toy example demonstrates a transition phenomenon for achieving any target probability for the set of potential maximizers.