Expectation-driven velocity adaptation promotes cooperation in mobile populations

Understanding how mobility interacts with local decision-making to shape the evolution of cooperation remains a central challenge in evolutionary game theory. In this work, we study a population of self-propelled agents moving on a continuous plane and playing a weak Prisoner’s Dilemma Game with dynamically changing neighbors. Agents adapt both their strategies and their migration velocities based on local payoff information. Specifically, we introduce a modified Bush–Mosteller learning rule in which agents compare their normalized payoffs with an internal expectation level and adjust their velocities asymmetrically depending on whether they are satisfied and which strategy they adopt. Numerical simulations show that this form of adaptive migration fundamentally reshapes the population’s spatiotemporal organization and markedly enhances the robustness of cooperation. Cooperators can survive under substantially higher temptation to defect than in systems with fixed velocities. Intermediate-high expectation values destabilize cooperation by promoting excessive and disordered movement, while low or full expectations stabilize it through distinct mechanisms. At low expectations, cooperators slow down and form dense, stationary clusters. At high expectations, coherent collective motion emerges and restores effective spatial reciprocity in the moving frame due to the synergistic interaction between direction alignment and velocity adaptation. Further analysis confirms that cooperation is maintained primarily through slow, clustered cooperators, while defectors remain more mobile and dispersed. These outcomes are robust against changes in population size and interaction radius, relying primarily on the resultant average interaction degree, together with the initial cooperator fraction and initial velocity distribution. Our work establishes expectation-driven velocity adaptation as a key regulatory mechanism for cooperation in mobile populations, highlighting that cooperative success depends not on how fast agents move, but on how they adapt their movement to strategic context and payoff feedback.