The conflicts in human societies have often been studied through evolutionary games. In social dilemmas, for example, individuals fair best if they defect, but the society is best off if everybody cooperates. Cooperation therefore often requires a mechanism or third parties to evolve and remain viable.

To study how third parties affect the evolution of cooperation, we develop a novel game theoretic framework composed of two layers. One layer contains cooperators and defectors, while the other, the third-party layer, contains interveners.

Interveners can be peacemakers, troublemakers, or a hybrid of these two. Focusing on two-player two-strategy games, we show that intervention, as an exogenous factor, can stimulate (or inhibit) cooperation by weakening (or strengthening) the dilemma strength of the game the disputant plays. Moreover, the outcome in the disputant layer that is triggered by intervention, in turn, stimulates its own evolution.

We analyze the co-evolution of intervention and cooperation and find that even a minority of interveners can promote higher cooperation. By conducting stability analyses, we derive the conditions for the emergence of cooperation and intervention.

Our research unveils the potential of third parties to control the evolution of cooperation.

H. Guo, Z. Song, M. Perc, Y. Li, Z. Wang, Third-Party Intervention of Cooperation in Multilayer Networks, IEEE Transactions on Systems, Man, and Cybernetics: Systems (2023).