Learning Nudges for Conditional Cooperation: A Multi-Agent Reinforcement Learning Model

Abstract

The public goods game describes a social dilemma in which a large proportion of agents act as conditional cooperators (CC): they only act cooperatively if they see others acting cooperatively because they satisfice with the social norm to be in line with what others are doing instead of optimizing cooperation. CCs are guided by aspiration-based reinforcement learning guided by past experiences of interactions with others and satisficing aspirations. In many real-world settings, reinforcing social norms do not emerge. In this paper, we propose that an optimizing reinforcement agent can facilitate cooperation through nudges, i.e. indirect mechanisms for cooperation to happen. The agent's goal is to motivate CCs into cooperation through its own actions to create social norms that signal that others are cooperating. We introduce a multi-agent reinforcement learning model for public goods games, with 3 CC learning agents using aspirational reinforcement learning and 1 nudging agent using deep reinforcement learning to learn nudges that optimize cooperation. For our nudging agent, we model two distinct reward functions, one maximizing the total game return (sum DRL) and one maximizing the number of cooperative contributions contributions higher than a proportional threshold (prop DRL). Our results show that our aspiration-based RL model for CC agents is consistent with empirically observed CC behavior. Games combining 3 CC RL agents and one nudging RL agent outperform the baseline consisting of 4 CC RL agents only. The sum DRL nudging agent increases the total sum of contributions by 8.22% and the total proportion of cooperative contributions by 12.42%, while the prop nudging DRL increases the total sum of contributions by 8.85% and the total proportion of cooperative contributions by 14.87%. Our findings advance the literature on public goods games and reinforcement learning.