Catalysts of Cooperation in System of Systems: The Role of Diversity and Network Structure

Cooperation and competition are critical aspects of complex systems that intrigue researchers and practitioners alike. Recently, there has been great interest in how structure affects these cooperative behaviors and how they evolve. In this paper, we utilize the methods of evolutionary game theory on graphs to develop a model of the structured evolution of adaptive agents. Rather than simple memoryless agents, we employ adaptive agents that take on a diverse set of strategies including the cooperative catalyst tit-for-tat (TFT) and its generous and suspicious variants. We also employ all-defect, unconditional cooperation, and random strategies. Agents use these strategies during their evolution in order to maximize their own relative fitness, measured by their performance in a repeated Prisoner´s Dilemma game versus their structural neighbors. We test the model with a variety of regular graph structures with variable degree, randomness, and size. Our parallel-execution agent-based simulations show that each strategy evolves toward its own structural niche with suspicious TFT maintaining the highest survival rate over all structures. We also show that increases in network density make the TFT strategies even more dominant, and connectivity randomness encourages cooperation in sparse networks.