Autocratic strategies in Cournot oligopoly game

2025-06-19

AI Summary

This paper investigates the existence of zero-determinant (ZD) strategies in infinitely repeated Cournot oligopoly games and their implications for tacit collusion. Using game-theoretic modeling and linear algebra techniques, we formally prove— for the first time—the existence of average unbeatable ZD strategies in this continuous-action setting. Combining analytical derivation with numerical simulations, we characterize strategy evolution under adaptive learning, both in single- and multi-learner environments. Results show that ZD strategies can unilaterally enforce linear payoff relationships, thereby controlling opponents’ long-run payoffs; in single-learner settings, they unexpectedly facilitate collusion by stabilizing collusive outcomes. However, in multi-learner dynamics, ZD strategies fail to sustain control and instead destabilize collusion, triggering noncooperative oscillations. Our work establishes the theoretical feasibility of ZD strategies in continuous-action oligopolies and, crucially, reveals their dual role in market coordination: while potentially reinforcing monopolistic cooperation, they may also provoke competitive instability. These findings offer novel insights for antitrust policy and regulatory design.

Technology Category

• Game Theory and Economic Paradigms: Coordination and Collaboration
• Multiagent Systems: Mechanism Design
• Machine Learning: Online Learning & Bandits

Application Category

• Economics, Online Markets and Human Computation: Social networks and social learning
• Web Mining and Content Analysis: Models for Web evolution
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

An oligopoly is a market in which the price of a goods is controlled by a few firms. Cournot introduced the simplest game-theoretic model of oligopoly, where profit-maximizing behavior of each firm results in market failure. Furthermore, when the Cournot oligopoly game is infinitely repeated, firms can tacitly collude to monopolize the market. Such tacit collusion is realized by the same mechanism as direct reciprocity in the repeated prisoner's dilemma game, where mutual cooperation can be realized whereas defection is favorable for both prisoners in one-shot game. Recently, in the repeated prisoner's dilemma game, a class of strategies called zero-determinant strategies attracts much attention in the context of direct reciprocity. Zero-determinant strategies are autocratic strategies which unilaterally control payoffs of players. There were many attempts to find zero-determinant strategies in other games and to extend them so as to apply them to broader situations. In this paper, first, we show that zero-determinant strategies exist even in the repeated Cournot oligopoly game. Especially, we prove that an averagely unbeatable zero-determinant strategy exists, which is guaranteed to obtain the average payoff of the opponents. Second, we numerically show that the averagely unbeatable zero-determinant strategy can be used to promote collusion when it is used against an adaptively learning player, whereas it cannot promote collusion when it is used against two adaptively learning players. Our findings elucidate some negative impact of zero-determinant strategies in oligopoly market.

Problem

• Existence of zero-determinant strategies in Cournot oligopoly
• Impact of unbeatable strategies on market collusion
• Negative effects of autocratic strategies in oligopolies

Innovation

• Zero-determinant strategies control payoffs unilaterally
• Averagely unbeatable strategy guarantees opponent's average payoff
• Promotes collusion against single adaptive player