Learning to Collude: A Folk Theorem for Algorithms

42 Pages Posted: 13 Dec 2022 Last revised: 30 Jan 2023

See all articles by Álvaro Cartea

Álvaro Cartea

University of Oxford; University of Oxford - Oxford-Man Institute of Quantitative Finance

Patrick Chang

University of Oxford - Oxford-Man Institute of Quantitative Finance

José Penalva

Universidad Carlos III, Madrid - Department of Business Administration

Harrison Waldon

The University of Texas at Austin; University of Oxford - Oxford-Man Institute of Quantitative Finance

Date Written: December 5, 2022

Abstract

We introduce state-dependent smooth fictitious play and we use this algorithm to prove a Folk theorem for repeated potential games under one-period perfect monitoring. Our result proves that decentralized learning algorithms can learn to collude through repeated interactions and without communication. Specifically, the algorithms learn to sustain a non-Nash supra-competitive outcome of the stage game by using a credible threat of punishment to suppress competition.

Keywords: Folk Theorem, Tacit Collusion, Stochastic Approximation, Smooth Fictitious Play

JEL Classification: C70, C72, C73, D21, D83

Suggested Citation

Cartea, Álvaro and Chang, Patrick and Penalva, José and Waldon, Harrison, Learning to Collude: A Folk Theorem for Algorithms (December 5, 2022). Available at SSRN: https://ssrn.com/abstract=4293831 or http://dx.doi.org/10.2139/ssrn.4293831

Álvaro Cartea

University of Oxford ( email )

Mansfield Road
Oxford, Oxfordshire OX1 4AU
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

Eagle House
Walton Well Road
Oxford, Oxfordshire OX2 6ED
United Kingdom

Patrick Chang (Contact Author)

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

Eagle House
Walton Well Road
Oxford, Oxfordshire OX2 6ED
United Kingdom

José Penalva

Universidad Carlos III, Madrid - Department of Business Administration ( email )

Calle Madrid 126
Getafe, 28903
Spain

Harrison Waldon

The University of Texas at Austin ( email )

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

Eagle House
Walton Well Road
Oxford, Oxfordshire OX2 6ED
United Kingdom

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