Evolutionary game dynamics under adaptive coordination

Decision-making in natural and artificial systems is often shaped by past interactions, as individuals adjust their behavior accordingly. A persistent challenge lies in identifying successful strategies and understanding how memory influences their performance, especially when individuals’ optimal actions conflict with collective outcomes. Most theoretical studies in evolutionary dynamics have focused on memory-1 strategies, and recent studies indicate that extending memory can improve strategies’ performance. Among these, all-or-none ( AoN K ) strategies perform well at short memory. Our analysis reveals, however, that their effectiveness deteriorates as memory extends, showing the inherent limitations of sole coordination. Building on this, we propose the adaptive coordination strategy, combining coordination and tolerance to enhance adaptability and stability. Our theoretical analysis precisely characterizes its behavior and key properties. This strategy outperforms classic memory-1 strategies and achieves optimal outcomes, providing a framework for understanding complex history-based behaviors beyond traditional memory- n models.