Reciprocal Reward Influence Encourages Cooperation From Self-Interested Agents

Emergent cooperation among self-interested individuals is a widespread phenomenon in the natural world, but remains elusive in interactions between artificially intelligent agents. Instead, na\"ive reinforcement learning algorithms typically converge to Pareto-dominated outcomes in even the simplest of social dilemmas. An emerging class of opponent-shaping methods have demonstrated the ability to reach prosocial outcomes by influencing the learning of other agents. However, they rely on higher-order derivatives through the predicted learning step of other agents or learning meta-game dynamics, which in turn rely on stringent assumptions over opponent learning rules or exponential sample complexity, respectively. To provide a learning rule-agnostic and sample-efficient alternative, we introduce Reciprocators, reinforcement learning agents which are intrinsically motivated to reciprocate the influence of an opponent's actions on their returns. This approach effectively seeks to modify other agents' $Q$-values by increasing their return following beneficial actions (with respect to the Reciprocator) and decreasing it after detrimental actions, guiding them towards mutually beneficial actions without attempting to directly shape policy updates. We show that Reciprocators can be used to promote cooperation in a variety of temporally extended social dilemmas during simultaneous learning.