Related papers: A Bridge between Bilevel Programs and Nash Games
An extensive literature in economics and social science addresses contests, in which players compete to outperform each other on some measurable criterion, often referred to as a player's score, or output. Players incur costs that are an…
Bilevel optimization has found successful applications in various machine learning problems, including hyper-parameter optimization, data cleaning, and meta-learning. However, its huge computational cost presents a significant challenge for…
In this paper, we consider stochastic monotone Nash games where each player's strategy set is characterized by possibly a large number of explicit convex constraint inequalities. Notably, the functional constraints of each player may depend…
Bilevel optimization, a hierarchical mathematical framework where one optimization problem is nested within another, has emerged as a powerful tool for modeling complex decision-making processes in various fields such as economics,…
We consider shared workspace scenarios with humans and robots acting to achieve independent goals, termed as parallel play. We model these as general-sum games and construct a framework that utilizes the Nash equilibrium solution concept to…
We revisit the complexity of deciding, given a {\it bimatrix game,} whether it has a {\it Nash equilibrium} with certain natural properties; such decision problems were early known to be ${\mathcal{NP}}$-hard~\cite{GZ89}. We show that…
In practical applications, decision-makers with heterogeneous dynamics may be engaged in the same decision-making process. This motivates us to study distributed Nash equilibrium seeking for games in which players are mixed-order (first-…
Game theory provides a well-established framework for the analysis of concurrent and multi-agent systems. The basic idea is that concurrent processes (agents) can be understood as corresponding to players in a game; plays represent the…
Bilevel optimization has witnessed a resurgence of interest, driven by its critical role in trustworthy and efficient AI applications. While many recent works have established convergence to stationary points or local minima, obtaining the…
We study the stochastic bilinear minimax optimization problem, presenting an analysis of the same-sample Stochastic ExtraGradient (SEG) method with constant step size, and presenting variations of the method that yield favorable…
Bilevel programs (BPs) find a wide range of applications in fields such as energy, transportation, and machine learning. As compared to BPs with continuous (linear/convex) optimization problems in both levels, the BPs with discrete decision…
We consider a bilevel problem involving two monotone equilibrium bifunctions and we show that this problem can be solved by a proximal point method with generalized proximal distances. We propose a framework for the convergence analysis of…
This paper develops a distributed Nash Equilibrium seeking algorithm for heterogeneous multi-robot systems. The algorithm utilises distributed optimisation and output control to achieve the Nash equilibrium by leveraging information shared…
Bilevel programs are optimization problems where some variables are solutions to optimization problems themselves, and they arise in a variety of control applications, including: control of vehicle traffic networks, inverse reinforcement…
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…
We investigate the complexity of bounding the uncertainty of graphical games, and we provide new insight into the intrinsic difficulty of computing Nash equilibria. In particular, we show that, if one adds very simple and natural additional…
We consider a stochastic generalized Nash equilibrium problem (GNEP) with expected-value cost functions. Inspired by Yi and Pavel (Automatica, 2019), we propose a distributed GNE seeking algorithm by exploiting the forward-backward operator…
We solve the stochastic generalized Nash equilibrium (SGNE) problem in merely monotone games with expected value cost functions. Specifically, we present the first distributed SGNE seeking algorithm for monotone games that requires one…
We propose fully-distributed algorithms for Nash equilibrium seeking in aggregative games over networks. We first consider the case where local constraints are present and we design an algorithm combining, for each agent, (i) the projected…
This work considers a stochastic Nash game in which each player solves a parameterized stochastic optimization problem. In deterministic regimes, best-response schemes have been shown to be convergent under a suitable spectral property…