For common notions of correlated equilibrium in extensive-form games, computing an optimal ( e.g., welfare-maximizing) equilibrium is NP-hard. Other equilibrium notions-- communication [11] and certification [12] equilibria--augment the game with a mediator that has the power to both send and receive messages to and from the players--and, in particular, to remember the messages. In this paper, we investigate both notions in extensive-form games from a computational lens. We show that optimal equilibria in both notions can be computed in polynomial time, the latter under a natural additional assumption known in the literature. Our proof works by constructing a mediator-augmented game of polynomial size that explicitly represents the mediator's decisions and actions.

We assume here that all agents share critic and actor networks, for notational convenience. Gaussian Distribution, from which an action is sampled, in continuous action spaces. In the loss functions above, B refers to the batch size and n refers to the number of agents. Multi-agent Particle-World Environment (MPE) was introduced in (Lowe et al., 2017). StarCraftII Micromanagement Challenge (SMAC) tasks were introduced in (Rashid et al., 2019).

Reinforcement Learning agent and a configurator that can modify some environmental parameters to improve the agent's performance.