A mechanism of dynamical interactions for two-person social dilemmas

We propose a new mechanism of interactions between game-theoretical agents in which the weights of the connections between interacting individuals are dynamical, payoff-dependent variables. Their evolution depends on the difference between the payoff of the agents from a given type of encounter and their average payoff. The mechanism is studied in the frame of two models: agents distributed on a random graph, and a mean field model. Symmetric and asymmetric connections between the agents are introduced. Long time behavior of both systems is discussed for the Prisoner's Dilemma and the Snow Drift games.