相关论文: A Log-domain Interior Point Method for Convex Quad…

This paper develops a unified framework for testing monotonicity of Bayesian Nash equilibrium strategies in unobserved types in games of incomplete information. We show that, under symmetric independent private types, monotonicity of…

The distributed computation of a Nash equilibrium in aggregative games is gaining increased traction in recent years. Of particular interest is the mediator-free scenario where individual players only access or observe the decisions of…

We present multilinear and mixed-integer multilinear programs to find a Nash equilibrium in multi-player noncooperative games. We compare the formulations to common algorithms in Gambit, and conclude that a multilinear feasibility program…

This paper develops a novel methodology to study robust stability properties of Nash equilibrium points in dynamic games. Small-gain techniques in modern mathematical control theory are used for the first time to derive conditions…

This paper is concerned with a non-zero sum differential game problem of an anticipated forward-backward stochastic differential delayed equation under partial information. We establish a necessary maximum principle and sufficient…

Data-driven modeling increasingly requires to find a Nash equilibrium in multi-player games, e.g. when training GANs. In this paper, we analyse a new extra-gradient method for Nash equilibrium finding, that performs gradient extrapolations…

Inspired by a paper of R. W. Rosenthal, we investigate generalized Nash-equilibria of integer programming games. We show that generalized Nash-equilibria always exist and are related to an optimal solution of a so-called N-fold integer…

This paper presents a novel data-driven approach for approximating the $\varepsilon$-Nash equilibrium in continuous-time linear quadratic Gaussian (LQG) games, where multiple agents interact with each other through their dynamics and…

This paper is concerned with two-person mean-field linear-quadratic non-zero sum stochastic differential games in an infinite horizon. Both open-loop and closed-loop Nash equilibria are introduced. Existence of an open-loop Nash equilibrium…

Game theory finds nowadays a broad range of applications in engineering and machine learning. However, in a derivative-free, expensive black-box context, very few algorithmic solutions are available to find game equilibria. Here, we propose…

We study generalized games with full row rank equality constraints and we provide a strikingly simple proof of strong monotonicity of the associated KKT operator. This allows us to show linear convergence to a variational equilibrium of the…

AI in Math deals with mathematics in a constructive manner so that reasoning becomes automated, less laborious, and less error-prone. For algorithms, the question becomes how to automate analyses for specific problems. For the first time,…

In this paper, we consider a distributed Bayesian Nash equilibrium (BNE) seeking problem in incomplete-information aggregative games, which is a generalization of Bayesian games and deterministic aggregative games. We handle the aggregation…

This paper investigates Nash equilibrium (NE) seeking problems for noncooperative games over multi-players networks with finite bandwidth communication. A distributed quantized algorithm is presented, which consists of local gradient play,…

Game theory has emerged as a powerful framework for modeling a large range of multi-agent scenarios. Many algorithmic solutions require discrete, finite games with payoffs that have a closed-form specification. In contrast, many real-world…

We consider a repeatedly played generalized Nash equilibrium game. This induces a multi-agent online learning problem with joint constraints. An important challenge in this setting is that the feasible set for each agent depends on the…

In this tutorial, we provide an introduction to machine learning methods for finding Nash equilibria in games with large number of agents. These types of problems are important for the operations research community because of their…

We consider a class of Wasserstein distributionally robust Nash equilibrium problems, where agents construct heterogeneous data-driven Wasserstein ambiguity sets using private samples and radii, in line with their individual risk-averse…

We develop a convex analysis approach for solving LQG optimal control problems and apply it to major-minor (MM) LQG mean-field game (MFG) systems. The approach retrieves the best response strategies for the major agent and all minor agents…

This paper proposes a new differentially private distributed Nash equilibrium seeking algorithm for aggregative games under time-varying unbalanced directed communication graphs. Random independent Laplace noises are injected into the…