Consensus and disagreement in collective homing problems: A mean field games formulation

Inspired by successful biological collective decision mechanisms such as honey bees searching for a new colony or the collective navigation of fish schools, we consider a mean field games (MFG) scenario producing decentralized homing decisions in large multi-agent systems. For our setup, we show that given an initial distribution of the agents, many strategies exist, with each one of them defining an ϵ-Nash equilibrium. These strategies, on which the processes of consensus and disagreement within the group depend, collapse into one strategy as the number of agents goes to infinity.