[Paper Review] Algorithmic Collusion in Cournot Duopoly Market: Evidence from Experimental Economics

Nan Zhou, Li Zhang+2 more|arXiv (Cornell University)|Feb 21, 2018

Evolutionary Game Theory and Cooperation14 references3 citations

TL;DR

This paper proposes a linear algorithm that exploits human behavior in a Cournot duopoly experiment to enforce tacit collusion, achieving higher long-term profits for the algorithm while reducing social welfare. It provides the first experimental evidence of algorithmic collusion emerging organically through strategic design, confirming its credibility as a real-world antitrust threat.

ABSTRACT

Algorithmic collusion is an emerging concept in current artificial intelligence age. Whether algorithmic collusion is a creditable threat remains as an argument. In this paper, we propose an algorithm which can extort its human rival to collude in a Cournot duopoly competing market. In experiments, we show that, the algorithm can successfully extorted its human rival and gets higher profit in long run, meanwhile the human rival will fully collude with the algorithm. As a result, the social welfare declines rapidly and stably. Both in theory and in experiment, our work confirms that, algorithmic collusion can be a creditable threat. In application, we hope, the frameworks, the algorithm design as well as the experiment environment illustrated in this work, can be an incubator or a test bed for researchers and policymakers to handle the emerging algorithmic collusion.

Motivation & Objective

• To investigate whether algorithmic agents can facilitate tacit collusion in human-algorithm markets, addressing a key gap in experimental economics.
• To provide empirical evidence on the credibility of algorithmic collusion as a threat to market competition.
• To develop and test a concrete algorithmic mechanism that can enforce collusion with human rivals in a controlled laboratory setting.
• To establish a testbed for antitrust regulation and algorithmic design by simulating real-world market dynamics.
• To highlight ethical and legal dilemmas arising when algorithmic collusion is economically rational yet socially harmful.

Proposed method

• Design a linear extortion strategy based on zero-determinant (ZD) principles, where the algorithm unilaterally controls the expected payoff ratio between itself and the human rival.
• Implement the algorithm in a 600-round repeated Cournot duopoly experiment with human participants, using a payoff-targeting mechanism defined by Equation (4).
• Use a controlled experimental framework (Figure 4) to simulate a market environment where the algorithm adjusts output to enforce collusion.
• Measure collusion through output levels, price trends, and deadweight loss to assess market efficiency.
• Compare algorithm-human collusion outcomes with historical human-human collusion data from long-run experiments.
• Apply theoretical expectations from game theory to validate the algorithm’s ability to extort cooperation through payoff manipulation.

Experimental results

Research questions

• RQ1 Can an algorithmically designed strategy enforce tacit collusion with a human rival in a Cournot duopoly market?
• RQ2 To what extent does the algorithm increase its own profit while inducing the human rival to collude?
• RQ3 How does algorithmic collusion affect social welfare, as measured by deadweight loss?
• RQ4 Is algorithmic collusion a credible threat, given that it emerges from rational human behavior under strategic pressure?
• RQ5 How does algorithm-human collusion compare to historical human-human collusion in terms of stability and efficiency?

Key findings

• The algorithm successfully extorted its human rival into colluding, resulting in sustained output reductions and price increases.
• The algorithm achieved a 29.6% higher profit than its human rival on average, confirming the payoff extortion mechanism (k = 1.296).
• Social welfare declined rapidly and stably, with deadweight loss increasing significantly over time.
• Collusion was observed to be stable and self-sustaining, driven by the human rival’s rational profit-maximization under algorithmic pressure.
• This study presents the first experimental observation of algorithmic collusion in a human-algorithm duopoly setting.
• The mechanism demonstrates that algorithmic collusion can emerge without explicit communication, challenging current legal distinctions between explicit and tacit collusion.