A Dynamic Game Model of Collective Choice in Multi-Agent Systems

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)-like scenario where a large number of agents have to make a choice among a set of different potential target destinations. Each individual both influences and is influenced by the group's decision, as well as the mean trajectory of all the agents. The model can be interpreted as a stylized version of opinion crystallization in an election for example. The agents' biases are dictated first by their initial spatial position and, in a subsequent generalization of the model, by a combination of initial position and a priori individual preference. The agents have linear dynamics and are coupled through a modified form of quadratic cost. Fixed point based finite population equilibrium conditions are identified and associated existence conditions are established. In general multiple equilibria may exist and the agents need to know all initial conditions to compute them precisely. However, as the number of agents increases sufficiently, we show that 1) the computed fixed point equilibria qualify as epsilon Nash equilibria, 2) agents no longer require all initial conditions to compute the equilibria but rather can do so based on a representative probability distribution of these conditions now viewed as random variables. Numerical results are reported

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

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 scenario where a large number of agents engaged in a dynamic game have to make a choice among a finite set of different potential target destinations. Each individual both influences and is influenced by the group's decision, as represented by the mean trajectory of all agents. Agents are assumed linear and coupled through a modified form of quadratic cost, whereby the terminal cost captures the discrete choice component of the problem. Following the mean field games methodology, we identify sufficient conditions under which allocations of destination choices over agents lead to self replication of the overall mean trajectory under the best response by the agents. Importantly, we establish that when the number of agents increases sufficiently, (i) the best response strategies to the self replicating mean trajectories qualify as epsilon-Nash equilibria of the population game; (ii) these epsilon-Nash strategies can be computed solely based on the knowledge of the joint probability distribution of the initial conditions, dynamics parameters and destination preferences, now viewed as random variables. Our results are illustrated through numerical simulations

Competition in Social Networks: Emergence of a Scale-free Leadership Structure and Collective Efficiency

Using the minority game as a model for competition dynamics, we investigate the effects of inter-agent communications on the global evolution of the dynamics of a society characterized by competition for limited resources. The agents communicate across a social network with small-world character that forms the static substrate of a second network, the influence network, which is dynamically coupled to the evolution of the game. The influence network is a directed network, defined by the inter-agent communication links on the substrate along which communicated information is acted upon. We show that the influence network spontaneously develops hubs with a broad distribution of in-degrees, defining a robust leadership structure that is scale-free. Furthermore, in realistic parameter ranges, facilitated by information exchange on the network, agents can generate a high degree of cooperation making the collective almost maximally efficient.Comment: 4 pages, 2 postscript figures include