Evolution of fairness in multi-objective reinforcement learning framework

Jingyi Zhang, Xin Ou, Guozhong Zheng, Shengfeng Deng, Jiqiang Zhang +1

Fairness, as a fundamental social norm, continues to pose a longstanding puzzle regarding its emergence. Traditional game-theoretic models largely rely on the assumption of \emph{Homo economicus}, wherein individuals are purely rational and self-interested, acting solely to maximize material payoffs. Such accounts, however, overlook the multidimensional nature of human decision-making, which is often shaped also by other considerations beyond economic incentives. To address this gap, we propose a multi-objective reinforcement learning framework that models the evolution of fairness as a dynamic trade-off between material payoff maximization and fairness-driven moral behavior, regulated by a fairness pressure coefficient. Using simulations of a two-objective Q-learning ultimatum game, we find that increased fairness pressure promotes fair outcomes, as expected. Strikingly, however, under moderate pressure, responder behavior reverses: responders become ``forgiving" by accepting low offers -- a pattern in line with our daily experience. Microscopic analyses reveal that this strategy reversal stems from competition between payoff-maximizing and fairness-oriented preferences. We…