Evolutionary Game Analysis of Educational Interactions in Digital Escape Room Games

Purpose This study explores how educational design can achieve a sustainable balance between challenge and support by synthesizing insights from multiple knowledge domains. Drawing on evolutionary game theory (EGT), learning theories such as flow and cognitive load, and the design principles of educational games and simulations, we investigate how learners, teachers, and digital platforms co-evolve their strategies in digital educational escape rooms (DEERs). Design/Methodology/Approach A tripartite evolutionary game model is developed to capture the interactions among learners, teachers, and platforms. The model uses payoff matrices and replicator dynamics to represent how strategic behaviors adapt over time, while stability analysis identifies which patterns of engagement are sustainable. Sensitivity analysis further examines the role of teacher feedback, gamification intensity, and learner participation costs. Findings Results demonstrate that stable learning environments emerge when challenge and support are carefully balanced. High teacher feedback sustains engagement under cognitively demanding tasks, while moderate combinations of teacher involvement and adaptive gamification yield evolutionarily stable strategies (ESS) that promote cooperation and persistence. Over-reliance on gamification increases cognitive load, whereas insufficient feedback diminishes learner motivation. Research Implications By positioning simulation as both a data generator and a research instrument, this work bridges game theory, educational psychology, and instructional design. It offers a theoretical framework for understanding how equilibrium strategies evolve in educational games and simulations more broadly, not only in digital escape rooms. Practical Implications The study provides actionable design insights for educators and platform developers. Specifically, it highlights how to calibrate difficulty, feedback, and gamification features to maintain flow, reduce cognitive overload, and foster long-term learner engagement. Originality/Value This article contributes a cross-domain synthesis by applying EGT and ESS to educational contexts, illustrating how mathematical modeling can inform practical design decisions. It introduces evolutionary stability as a guiding concept for structuring engaging and effective educational game environments across digital, hybrid, and face-to-face modalities.