Game interactions and dynamics on networked populations

A new mathematical formulation of evolutionary game dynamics on networked populations is proposed. The model extends the standard replicator equation to a finite set of players organized on an arbitrary network of connections (graph). Classical results of multipopulation evolutionary game theory are used in combination with graph theory to obtain the mathematical model. Specifically, the players, located at the vertices of the graph, are interpreted as subpopulations of a multipopulation dynamical game. The members of each subpopulation are replicators, engaged at each time instant into 2-player games with the members of other connected subpopulations. This idea allows us to write an extended equation describing the game dynamics of a finite set of players connected by a graph. The obtained equation does not require any assumption on the game payoff matrices nor graph topology. Stability of steady states, Nash equilibria and the relationship of the proposed model to the standard replicator equation are discussed. The dynamical behavior of the model over different graphs is also investigated by means of extended simulations.