Chiara Mocenni (Università di Siena)
Game Interactions and Dynamics on Complex Networks
The talk presents an extension of the mathematical formulation of evolutionary game dynamics to networked populations. The model, grounded on the standard replicator equation, is modified in order to account for the dynamics of a finite set of players organized in a network of connections (graph). In the proposed framework, the players are located at the vertices of the graph and are modeled as subpopulations of a multipopulation game. Moreover, the dynamical equations are derived by assuming that couples of members belonging to two different and connected subpopulations are engaged at each time instant in two-players games. The obtained equations describe the strategic interactions of a finite set of individuals connected in a graph, without any assumptions on the game payoff matrices and on the adjacency matrix of the graph. The stability of steady states, the existence of Nash equilibria and the presence of evolutionary stable strategies are discussed. The dynamical behavior of the solutions and the potentialities of the model are also investigated by means of extended simulations. Finally, the obtained equations are used for explaining the mechanisms of bacterial aggregation leading to the formation of biofilms.