Multi-Agent Coordination under Poisson Observations: A Global Game Approach

TL;DR

This paper models strategic coordination among multiple agents with Poisson-distributed signals using a global game framework, demonstrating equilibrium existence and analyzing potential functions, with applications to bacterial Quorum Sensing systems.

Contribution

It introduces a global game approach to multi-agent coordination with Poisson observations, proving equilibrium existence and analyzing potential functions for infinite-agent systems.

Findings

Existence of Bayesian Nash equilibrium in threshold policies.

Potential function is unimodal with a clear maximum.

Applicable to modeling bacterial Quorum Sensing systems.

Abstract

We study a model of strategic coordination based on a class of games with incomplete information known as Global Games. Under the assumption of Poisson-distributed signals and a Gamma prior distribution on state of the system, we demonstrate the existence of a Bayesian Nash equilibrium within the class of threshold policies for utility functions that are linear in the agents' actions. Although computing the exact threshold that constitutes an equilibrium in a system with finitely many agents is a highly non-trivial task, the problem becomes tractable by analyzing the game's potential function with countably infinitely many agents. Through numerical examples, we provide evidence that the resulting potential function is unimodal, exhibiting a well-defined maximum. Our results are applicable to the modeling of bacterial Quorum Sensing systems, whose noisy observation signals are often well-approximated using Poisson processes.