Cooperation, structure, and hierarchy in multiadaptive games.

Game-theoretical models where the rules of the game and the interaction structure both coevolve with the game dynamics--multiadaptive games--capture very flexible situations where cooperation among selfish agents can emerge. In this work, we will discuss a multiadaptive model presented in a recent Letter [Phys. Rev. Lett. 106, 028702 (2011)] as well as generalizations of it. The model captures a nonequilibrium situation where social unrest increases the incentive to cooperate and, simultaneously, agents are partly free to influence with whom they interact. First, we investigate the details of how feedback from the behavior of agents determines the emergence of cooperation and hierarchical contact structures. We also study the stability of the system to different types of noise, and find that different regions of parameter space show very different response. Some types of noise can destroy an all-cooperator (C) state. If, on the other hand, hubs are stable, then so is the all-C state. Finally, we investigate the dependence of the ratio between the time scales of strategy updates and the evolution of the interaction structure. We find that a comparatively fast strategy dynamics is a prerequisite for the emergence of cooperation.