Game-based coalescence over multi-agent systems

TL;DR

This paper models the coalescence process in multi-agent systems using game theory, proving almost sure convergence and analyzing coalescence time with theoretical and simulation validation.

Contribution

It introduces a game-theoretic framework for analyzing coalescence in rational agents, including proof of almost sure coalescence and time distribution analysis.

Findings

Agents coalesce into one group with probability one.

Expected coalescence time is derived for power payoff functions.

Simulation results validate theoretical predictions.

Abstract

Coalescence, as a kind of ubiquitous group behavior in the nature and society, means that agents, companies or other substances keep consensus in states and act as a whole. This paper considers coalescence for n rational agents with distinct initial states. Considering the rationality and intellectuality of the population, the coalescing process is described by a bimatrix game which has the unique mixed strategy Nash equilibrium solution. Since the process is not an independent stochastic process, it is difficult to analyze the coalescing process. By using the first Borel-Cantelli Lemma, we prove that all agents will coalesce into one group with probability one. Moreover, the expected coalescence time is also evaluated. For the scenario where payoff functions are power functions, we obtain the distribution and expected value of coalescence time. Finally, simulation examples are provided to validate the effectiveness of the theoretical results.