Algorithmic Collusion and a Folk Theorem from Learning with Bounded Rationality

40 Pages Posted: 13 Dec 2022 Last revised: 17 Apr 2024

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

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

Date Written: December 5, 2022

Abstract

We prove a Folk theorem when players with bounded rationality learn as they play a repeated potential game. We use a dynamic generalization of smooth fictitious play with bounded m-memory strategies to model learning with bounded rationality that is consistent with learning by algorithms. In a repeated potential game with perfect monitoring, we use this learning model to show that for any feasible and individually rational payoff profile, if players have sufficient memory, are sufficiently patient, and best respond with sufficiently few mistakes, then the players have a non-zero probability of learning an m-memory strategy profile that achieves an average payoff close to the specified payoff profile for an appropriate continuation game. Moreover, the strategy profile learned is an m-memory ε-subgame perfect equilibrium of the repeated game. This finding demonstrates that competition authorities are correct in their concern about algorithmic collusion.

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, Algorithmic Collusion and a Folk Theorem from Learning with Bounded Rationality (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

University of Texas at Austin ( email )

Texas

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

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

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
621
Abstract Views
1,823
Rank
82,769
PlumX Metrics