Learning Correlated Equilibrium Via Neural Network Regret Minimisation

This paper studies how decentralised neural agents trained by regret minimisation learn equilibrium behaviour in static games and whether such learning can be extended beyond Nash equilibria. The analysis proceeds in two parts. The first chapter examines equilibrium selection in coordination games with multiple Nash equilibria. Building on recent evidence that neural agents trained across large distributions of games systematically favour risk-dominant equilibria, the chapter introduces a structured pre-training curriculum designed to instil a bias toward payoffdominant outcomes in Stag Hunt environments. While pre-training successfully induces effcient coordination in these games, the results show that this bias is rapidly eroded under subsequent adversarial training on heterogeneous games, where play reverts to mixed or risk-sensitive equilibria. The second chapter investigates whether decentralised learners can acquire correlated equilibrium behaviour when coordination requires conditioning on private signals. Initial experiments demonstrate that standard personal regret objectives lead agents to ignore mediator signals and converge to unconditional Nash strategies. This limitation is overcome by replacing personal regret with a squared obedience (swap) regret objective. Under this modified objective, neural agents successfully learn signal-contingent behaviour and generalise correlated equilibrium strategies to unseen coordination games. Together, the findings clarify the capabilities and limitations of regret-based learning as a mechanism for equilibrium formation in strategic environments.