A dynamic game model of collective choice in multi-agent systems

Inspired by socially influenced decision making mechanisms such as the collective behavior of cancer cells, honey bees searching for a new colony or the mobility of bacterial swarms, we consider a Mean Field Games (MFG) model of collective choice where a large number of agents choose between multiple alternatives while taking into account the group's behavior. For example, in elections, individual interests and collective opinion swings together contribute in the crystallization of final decisions. At first, the agents' decisions are determined by their initial states. Subsequently, the model is generalized to include a priori individual preferences towards the destination points. For example, personal preferences that transcend party lines in elections. We show that multiple strategies exist with each one of them defining an epsilon Nash equilibrium.