Beyond the prisoner’s dilemma: Cooperation in repeated three-action games

Conflicts of interest arise across biology, social sciences, and artificial intelligence, where self-interested agents often struggle to resolve them, leading to socially inefficient outcomes. In game theory and evolutionary game theory, the iterated prisoner’s dilemma (IPD) has long served as the canonical model for studying such dilemmas. Yet, despite its central role, the two-action IPD oversimplifies real-world interactions. By contrast, multi-action models are better suited to capture the richness of adaptive behavior, but systematic theoretical work in this direction remains scarce, as extending the action space greatly complicates both theoretical and simulation analyses. We advance this line of research by extending the IPD framework to an n-player, three-action setting, through which we identify cooperative equilibria that emerge more readily—those sustaining fair outcomes as Nash equilibria over a wider parameter domain—and reveal a fundamental mechanism for conflict resolution. In particular, our analysis identifies conditions under which partner equilibria can be sustained more readily in three-action games than in two-action ones. We further conduct an evolutionary analysis in which agents learn by imitating higher-performing strategies, revealing how adaptive behavior enables them to align incentives with opponents and promote fair and efficient outcomes even when opponents pursue only their own payoffs. Taken together, our results advance the theoretical foundations of repeated multi-action games and offer insights into how fairness and cooperation can emerge in multiagent systems characterized by conflicting interests.