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 article, we analyze a simple version of the
best experienced payoff
(BEP) algorithm, a revision protocol that has recently been 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 strategies, and we analyze the robustness of the algorithm to different updating schemes (e.g., synchronous versus asynchronous) and to different types of interaction networks (e.g., ring, preferential attachment, small world, and complete). In all the 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.