Related papers: Regularized Gradient Descent Ascent for Two-Player…

Many economic games and machine learning approaches can be cast as competitive optimization problems where multiple agents are minimizing their respective objective function, which depends on all agents' actions. While gradient descent is a…

Subgame solving is a technique for scaling algorithms to large games by locally refining a precomputed blueprint strategy during gameplay. While straightforward in perfect-information games where search starts from the current state,…

We consider the problem of computing stationary points in min-max optimization, with a particular focus on the special case of computing Nash equilibria in (two-)team zero-sum games. We first show that computing $\epsilon$-Nash equilibria…

Many emerging applications - such as adversarial training, AI alignment, and robust optimization - can be framed as zero-sum games between neural nets, with von Neumann-Nash equilibria (NE) capturing the desirable system behavior. While…

In this paper, we study the distributed generalized Nash equilibrium seeking problem of non-cooperative games in dynamic environments. Each player in the game aims to minimize its own time-varying cost function subject to a local action…

This paper proposes a novel approach for local convergence to Nash equilibrium in quadratic noncooperative games based on a distributed Lie-bracket extremum seeking control scheme. This is the first instance of noncooperative games being…

This paper studies a type of rank-based mean field game in which competing agents strategically switch among multiple effort regimes. We propose an entropy regularized auxiliary problem where the switching decisions are randomized to the…

In this paper, we consider two-player zero-sum matrix and stochastic games and develop learning dynamics that are payoff-based, convergent, rational, and symmetric between the two players. Specifically, the learning dynamics for matrix…

Auctions are modeled as Bayesian games with continuous type and action spaces. Determining equilibria in auction games is computationally hard in general and no exact solution theory is known. We introduce an algorithmic framework in which…

The standard risk minimization paradigm of machine learning is brittle when operating in environments whose test distributions are different from the training distribution due to spurious correlations. Training on data from many…

We study the convergence of Optimistic Gradient Descent Ascent in unconstrained bilinear games. In a first part, we consider the zero-sum case and extend previous results by Daskalakis et al. in 2018, Liang and Stokes in 2019, and others:…

We study constrained bi-matrix games, with a particular focus on low-rank games. Our main contribution is a framework that reduces low-rank games to smaller, equivalent constrained games, along with a necessary and sufficient condition for…

Gradient flows play a substantial role in addressing many machine learning problems. We examine the convergence in continuous-time of a \textit{Fisher-Rao} (Mean-Field Birth-Death) gradient flow in the context of solving convex-concave…

We show that an N-person non-cooperative semi-Markov game under limiting ratio average pay-off has a pure semi-stationary Nash equilibrium. In an earlier paper, the zero-sum two person case has been dealt with. The proof follows by reducing…

This paper proposes a new mathematical paradigm to analyze discrete-time mean-field games. It is shown that finding Nash equilibrium solutions for a general class of discrete-time mean-field games is equivalent to solving an optimization…

In this paper, we investigate a distributed Nash equilibrium computation problem for a time-varying multi-agent network consisting of two subnetworks, where the two subnetworks share the same objective function. We first propose a…

Successful algorithms have been developed for computing Nash equilibrium in a variety of finite game classes. However, solving continuous games -- in which the pure strategy space is (potentially uncountably) infinite -- is far more…

Recent advances at the intersection of dense large graph limits and mean field games have begun to enable the scalable analysis of a broad class of dynamical sequential games with large numbers of agents. So far, results have been largely…

We consider a class of concave continuous games in which the corresponding admissible strategy profile of each player underlies affine coupling constraints. We propose a novel algorithm that leads the relevant population dynamic toward Nash…

There are only limited classes of multi-player stochastic games in which independent learning is guaranteed to converge to a Nash equilibrium. Markov potential games are a key example of such classes. Prior work has outlined sets of…