Optimizing Coordination among Bounded Rational Agents

Coordination is a desirable feature in many multi-agent systems, such as robotic and socioeconomic networks. Traditionally, these agents are assumed to be perfectly rational, i.e., they are designed and trained to maximize their expected utilities. However, in many situations, perfectly rational behavior is not possible. We consider a binary networked coordination game over a weighted undirected regular graph with a sparsity constraint. Each agent exhibits bounded rationality and employs a distributed stochastic learning algorithm known as {\it Log Linear Learning} to update its action conditioned on the actions currently played by its neighbors. We optimize the probability that the multi-agent system will converge to a pure Nash equilibria of the game with respect to the graph weights. We provide analytical and numerical results for specific sparsity patterns considered in a classical behavioral economics experiment from Leavitt and Bavellas (1951).