The algorithmic learning equations

This thesis presents the Algorithmic Learning Equations (ALEs) to study tacit algorithmic collusion. The ALEs are a set of differential equations that characterizes the finite-time and asymptotic behavior of state-dependent learning algorithms in stochastic and repeated games. The ALEs are derived rigorously, drawing upon stochastic approximation theory. The ALEs are analyzed to show, numerically and theoretically, that decentralized, self-interested learning algorithms can learn to collude. The final chapter of this thesis presents preliminaries using inverse reinforcement learning to detect collusion in a data-driven way. The contents of this thesis are primarily drawn from joint work with Professor Álvaro Cartea, Professor José Penalva, and Patrick Chang during various research visits to the Oxford-Man Institute of Quantitative Finance in 2022 and 2023.