The Prisoner's Dilemma in Price Wars: A Game Analysis Based on Competition in a Duopoly Market

In a duopoly market, price wars between firms often lead to a "prisoner's dilemma" due to non-cooperative game dynamics, creating a conflict between individual and collective rationality. Based on game theory, this paper constructs static and dynamic game models to analyze the strategic choices and equilibrium outcomes of duopolistic firms in price competition. The study finds that under complete-information static games, both firms tend to adopt price-cutting strategies to gain market share, resulting in a Nash equilibrium of "low-price competition." However, this equilibrium deviates from Pareto optimality, leading to mutual profit losses and revealing the prisoner's dilemma nature of price wars. Under an infinitely repeated game framework, firms may overcome short-term profit constraints through trigger strategies or reputation mechanisms, achieving long-term cooperation and mutual benefits. Furthermore, through case studies, the paper explores how market transparency, regulatory policies, and strategic rule design can mitigate this dilemma, proposing feasible approaches such as signaling mechanisms and punishment schemes to foster cooperative competition. This research provides a theoretical foundation for understanding pricing strategies and offers practical insights for optimizing market competition and antitrust policy formulation.