Quantifying the Self-Interest Level of Markov Social Dilemmas

Abstract: This paper introduces a novel method for estimating the self-interest level of Markov social dilemmas. We extend the concept of self-interest level from normal-form games to Markov games, providing a quantitative measure of the minimum reward exchange required to align individual and collective interests. We demonstrate our method on three environments from the Melting Pot suite, representing either common-pool resources or public goods. Our results illustrate how reward exchange can enable agents to transition from selfish to collective equilibria in a Markov social dilemma. This work contributes to multi-agent reinforcement learning by providing a practical tool for analysing complex, multistep social dilemmas. Our findings offer insights into how reward structures can promote or hinder cooperation, with potential applications in areas such as mechanism design.