Fast and Scalable Global Convergence in Single-Optimum Decentralized Coordination Problems

Over the past few years, the scientific community has been studying the usefulness of evolutionary game theory to solve distributed control problems. In this paper we analyze a simple version of the Best Experienced Payoff (BEP) algorithm, a revision protocol recently proposed in the evolutionary game theory literature. This revision protocol is simple, completely decentralized and has minimum information requirements. Here we prove that adding some noise to this protocol can lead to efficient results in single-optimum coordination problems in little time, even in large populations of agents. We also test the algorithm under a wide range of different conditions using computer simulation. In particular, we consider different numbers of agents and of strategies, and we analyze the robustness of the algorithm to different updating schemes (e.g. synchronous vs asynchronous) and to different types of interaction networks (e.g. ring, preferential attachment, small world and complete). In all cases, using the noisy version of BEP, the agents quickly approach a small neighborhood of the optimal state from every initial condition, and spend most of the time in that neighborhood.Financial support from the Spanish State Research Agency (PID2020-118906GBI00/AEI/10.13039/501100011033), from the Regional Government of Castilla y Leon and the EU-FEDER program (CLU-2019-04), from the ´ Spanish Ministry of Science, Innovation and Universities, and from the Fulbright Program (PRX19/00113, PRX21/00295), is gratefully acknowledged