Decoding fairness: a reinforcement learning perspective

Abstract: Behavioral experiments on the ultimatum game (UG) reveal that we humans prefer fair acts, which contradicts the prediction made in orthodox Economics. Existing explanations, however, are mostly attributed to exogenous factors within the imitation learning framework. Here, we adopt the reinforcement learning paradigm, where individuals make their moves aiming to maximize their accumulated rewards. Specifically, we apply Q-learning to UG, where each player is assigned two Q-tables to guide decisions for the roles of proposer and responder. In a two-player scenario, fairness emerges prominently when both experiences and future rewards are appreciated. In particular, the probability of successful deals increases with higher offers, which aligns with observations in behavioral experiments. Our mechanism analysis reveals that the system undergoes two phases, eventually stabilizing into fair or rational strategies. These results are robust when the rotating role assignment is replaced by a random or fixed manner, or the scenario is extended to a latticed population. Our findings thus conclude that the endogenous factor is sufficient to explain the emergence of fairness, exogenous factors are not needed.