We resolve the question of the complexity of Nash equilibrium by showing that the problem of computing a Nash equilibrium in a game with 4 or more players is complete for the complexity class PPAD.Expand

We address the issue of limit cycling behavior in training Generative Adversarial Networks and propose the use of Optimistic Mirror Decent (OMD) for Wasserstein GANs.Expand

We show that finding a Nash equilibrium in three-player games is indeed PPAD-complete; and we do so by a reduction from Brouwer's problem, thus establishing that the two problems are computationally equivalent.Expand

We give a simple, linear-time algorithm examining just two strategies per player and resulting in a 12-approximate Nash equilibrium in any 2-player game.Expand

We show that every feasible, Bayesian, multi-item multi-bidder mechanism for independent, additive bidders can be implemented as a mechanism that: (a) allocates every item independently of the other items; (b) for the allocation of each item it uses a strict ordering of all bbiders' types; and allocates the item using a distribution over hierarchical mechanisms that iron this ordering into a non-strict ordering.Expand

We provide a duality-based framework for revenue maximization in a multiple-good monopoly and prove that the optimal values of these problems are always equal.Expand

We give a polynomial algorithm for computing an Îµ-approximate Nash equilibrium in 2-player games with Îµ â‰ˆ .38; our algorithm computes equilibria with arbitrarily large supports.Expand