Altruism and Fair Objective in Mixed-Motive Markov games

Yao-hua Franck XU, Tayeb LEMLOUMA, Arnaud Braud, Jean-Marie Bonnin

Keywords: Social Dilemma, Game Theory, Markov Game, Multi-agent Reinforcement Learning, Fairness

Abstract:

Cooperation is fundamental in society's viability, as it enables the emergence of structure within heterogeneous groups that seek collective well-being. However, individuals are inclined to defect in order to benefit from the group's cooperation without contributing the associated costs, thus leading to unfair situations. In game theory, social dilemmas entail this dichotomy between individual interest and collective outcome. The most dominant approach to multi-agent cooperation is the utilitarian welfare which can produce efficient but highly inequitable outcomes.

This paper proposes a novel framework to foster fairer cooperation by replacing the standard utilitarian objective with Proportional Fairness. We introduce a fair altruistic utility for each agent, defined on the individual log-payoff space and derive the analytical conditions required to ensure cooperation in classic social dilemmas. We then extend this framework to sequential settings by defining a Fair Altruistic Markov Game and deriving novel fair Actor-Critic algorithms to learn fair policies. Finally, we evaluate our method in various social dilemma environments.

Area: Learning and Adaptation (LEARN)

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Submission Number: 1701