Cooperation, social networks, and the emergence of leadership in a prisoner's dilemma with adaptive local interactions.

Cooperative behavior among a group of agents is studied assuming adaptive interactions. Each agent plays a Prisoner's Dilemma game with its local neighbors, collects an aggregate payoff, and imitates the strategy of its best neighbor. Agents may punish or reward their neighbors by removing or sustaining the interactions, according to their satisfaction level and strategy played. An agent may dismiss an interaction, and the corresponding neighbor is replaced by another randomly chosen agent, introducing diversity and evolution to the network structure. We perform an extensive numerical and analytical study, extending results in M. G. Zimmermann, V. M. Eguíluz, and M. San Miguel, Phys. Rev. E 69, 065102(R) (2004). We show that the system typically reaches either a full-defective state or a highly cooperative steady state. The latter equilibrium solution is composed mostly by cooperative agents, with a minor population of defectors that exploit the cooperators. It is shown how the network adaptation dynamics favors the emergence of cooperators with the highest payoff. These "leaders" are shown to sustain the global cooperative steady state. Also we find that the average payoff of defectors is larger than the average payoff of cooperators. Whenever "leaders" are perturbed (e.g., by addition of noise), an unstable situation arises and global cascades with oscillations between the nearly full defection network and the fully cooperative outcome are observed.