Several works have investigated the influence of graph topology on cooperation among artificial agents, while the majority of the literature has focused on modelling agents' adaptation through strategy imitation, which relies solely on the cumulative payoffs of others. This paper investigates scenarios in which each agent learns to play the two-player Iterated Prisoner's Dilemma (IPD) using deep reinforcement learning. Each agent is represented as a node in a graph, where its neighbours constitute the pool of opponents with whom it can interact. During each IPD episode, agents are provided with different types of information about their opponent, consisting of action history and opponent identity. Experimental results across different graph topologies show that the number of neighbours per node and the average path length are the main factors affecting the emergence of cooperation. We also show that, while partner selection fosters mutual cooperation by limiting the diversity of the opponent pool, providing agents with the identity of their opponent hinders the proliferation of cooperative strategies.
Inducing cooperation among distributed agents is still a difficult problem in the field of multi-agent reinforcement learning (MARL), particularly in social dilemma situations. There, individual interests are misaligned with the common good and individual rationality leads to suboptimal group outcomes. In contrast, humans are able to achieve cooperation with one another in such situations. A common explanation for such cooperative behavior is that individuals have social preferences. In order to achieve cooperation in MARL, we design a new utility function integrating altruistic preferences (incentive for other's reward) and fairness preferences (incentive for equality) from social psychology and behavioral economics, namely, Altruistic and Fairness Preference (AFP), a reward-sharing mechanism which converts one's own and other's rewards to incentives for cooperative behavior. We performed comparative experiments with standard RL and inequity aversion agents in two challenging sequential social dilemma games, and showed that AFP agents successfully achieved mutual cooperation with more collective rewards and higher equity than the baselines. To further understand the progression of AFP during training, we subsequently explore the effects of altruistic preferences and fairness preferences on agents' behavior. The results suggest that altruistic preferences encourage agents to contribute to the public goods, and fairness preferences induce mutual behavior between agents.