Learning to Collude: A Folk Theorem for Algorithms

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