Q-learning promotes the evolution of fairness and generosity in the ultimatum game

The traditional Q-learning algorithm has been widely applied to the study of cooperation in social dilemmas, however, few studies have utilized it in the context of the Ultimatum Game. To address this gap, this paper investigates the evolutionary Ultimatum Game by proposing a strategy-adjustment-based Q-learning algorithm. Through Monte Carlo simulations, we quantitatively confirm the significant influence of sensitivity factors (denoted as ${\beta }_p$ and ${\beta }_q$) on fairness and generosity. Notably, compared to the conventional situation, the introduction of sensitivity factors, especially when ${\beta }_p\gg {\beta }_q$, leads to a marked increase in levels of fairness and generosity. Additionally, when ${\beta }_p\ll {\beta }_q$, the population gravitates toward empathy-driven strategies, further enhancing fairness. Conversely, we find that when ${\beta }_p$ and ${\beta }_q$ are approximately equal, fairness is undermined. These evolutionary dynamics provide deeper insights into the mechanisms underlying fairness and generosity in human behavior.