Evolutionary dynamics of memory-based strategies in repeated and structured social interactions (2509.10820v1)

Abstract: Human social life is shaped by repeated interactions, where past experiences guide future behavior. In evolutionary game theory, a key challenge is to identify strategies that harness such memory to succeed in repeated encounters. Decades of research have identified influential one-step memory strategies (such as Tit-for-Tat, Generous Tit-for-Tat, and Win-Stay Lose-Shift) that promote cooperation in iterated pairwise games. However, these strategies occupy only a small corner of the vast strategy space, and performance in isolated pairwise contests does not guarantee evolutionary success. The most effective strategies are those that can spread through a population and stabilize cooperation. We propose a general framework for repeated-interaction strategies that encompasses arbitrary memory lengths, diverse informational inputs (including both one's own and the opponent's past actions), and deterministic or stochastic decision rules. We analyze their evolutionary dynamics and derive general mathematical results for the emergence of cooperation in any network structure. We then introduce a unifying indicator that quantifies the contribution of repeated-interaction strategies to population-level cooperation. Applying this indicator, we show that long-memory strategies evolve to promote cooperation more effectively than short-memory strategies, challenging the traditional view that extended memory offers no advantage. This work expands the study of repeated interactions beyond one-step memory strategies to the full spectrum of memory capacities. It provides a plausible explanation for the high levels of cooperation observed in human societies, which traditional one-step memory models cannot account for.