Cooperation is fundamental for 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 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 Markov Game and deriving novel fair Actor-Critic algorithms to learn fair policies. Finally, we evaluate our method in various social dilemma environments.

翻译：合作是社会存续的根基，它使得追求集体福祉的异质群体内部能够形成结构。然而，个体倾向于通过背叛行为，在不承担相应成本的情况下从群体合作中获益，从而导致不公平局面。在博弈论中，社会困境体现了个人利益与集体结果之间的这种二元对立。当前多智能体合作的主流方法是功利主义福利，其可能产生高效但高度不公平的结果。本文提出一种新颖框架，通过以比例公平性替代标准的功利主义目标，促进更公平的合作。我们为每个智能体引入一种公平的利他主义效用函数，该函数定义于个体对数收益空间，并推导了在经典社会困境中确保合作所需的分析条件。随后，我们将此框架扩展至序贯决策场景，通过定义公平马尔可夫博弈并推导新型公平行动者-评论家算法来学习公平策略。最后，我们在多种社会困境环境中对所提方法进行了评估。