  Game-theoretical models where the rules of the game and the interaction
structure both coevolves 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)], and generalizations of it.
The model captures a non-equilibrium 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 the
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
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 timescales 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.
