Hierarchical Incentives and the Evolution of Local Cooperation in Wartime: A Continuous Strategy Approach
Historical episodes such as the World War I "live-and-let-live" system and the Christmas Truce of 1914 demonstrate that opposing military units can establish spontaneous, local cooperation even in extreme conflict environments. Such cooperative behavior is typically fragile and temporary, while large-scale wars persist. We develop a hierarchical decision problem in which local units adopt contingent strategies that depend on interactions, accumulated payoffs, and signals from a central command. The command authority can impose enforcement that penalizes non-aggression to prolong hostilities. Our model features a continuous space of parametric strategies and formalizes replicator dynamics over the population. We analytically characterize the conditions under which local cooperation emerges as a stable evolutionary equilibrium and identify critical thresholds of central enforcement that destroy cooperative equilibria. We show that stable peace requires either alignment of command incentives with frontline welfare, external constraints on enforcement, or diminishing political returns to conflict. The framework provides a micro-founded explanation for the persistence of war despite locally beneficial cooperation.