This was an overall nice and fun paper to read. The problem was well-motivated and the background well-covered. Possibly some important definitions were skipped (such as sequence form) but with space constraints I feel the authors chose the right level of abstraction for presentation (leaving the right amount of detail for the appendix). One (fairly minor) concern is that the scope is a bit narrow. There is a small community working on these notions of equilibria, and addressing only the 2-player case without chance feels like a bit restrictive, given previous simple algorithms that solve the n-player setting such as Dudik & Gordon.

While Nash equilibrium in extensive-form games is well understood, very little is known about the properties of extensive-form correlated equilibrium (EFCE), both from a behavioral and from a computational point of view. In this setting, the strategic behavior of players is complemented by an external device that privately recommends moves to agents as the game progresses; players are free to deviate at any time, but will then not receive future recommendations. First, we show that an EFCE can be formulated as the solution to a bilinear saddle-point problem. To showcase how this novel formulation can inspire new algorithms to compute EFCEs, we propose a simple subgradient descent method which exploits this formulation and structural properties of EFCEs. Our method has better scalability than the prior approach based on linear programming.