A Folk Theorem from Learning in Games


We introduce a generalisation of smooth fictitious play with bounded m-memory strategies. We use this learning algorithm to prove a Folk theorem from learning in repeated potential games. If a payoff profile is supported by an m-memory pure strategy subgame perfect equilibrium, then there is a non-zero probability of learning an m-memory strategy profile that is arbitrarily close to the desired equilibrium, so that the desired payoff profile is (approximately) achieved in an appropriate continuation game. Our results prove that autonomous artificial agents who use a learning process to develop strategies to play the game can learn to collude.


Patrick Chang is a PhD student at the Oxford-Man Institute under the supervision of Professor Álvaro Cartea.

His research aims to understand the interaction of multiple autonomous agents, and the impact and risk these interactions have on the broader economy and financial markets. Of particular interest, is whether the agents learn to collude or manipulate markets, and whether we can detect and prevent these unintended consequences to protect social welfare and improve market efficiency.


12 April 2023