Fictitious Play Outperforms Counterfactual Regret Minimization

We compare the performance of two popular algorithms, fictitious play and counterfactual regret minimization, in approximating Nash equilibrium in multiplayer games. Despite recent success of counterfactual regret minimization in multiplayer poker and conjectures of its superiority, we show that fictitious play leads to improved Nash equilibrium approximation over a variety of game classes and sizes.