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Nash equilibrium is one of the most influential solution concepts in game theory. With the development of computer science and artificial intelligence, there is an increasing demand on Nash equilibrium computation, especially for Internet…
Constrained quasiconvex optimization problems appear in many fields, such as economics, engineering, and management science. In particular, fractional programming, which models ratio indicators such as the profit/cost ratio as fractional…
In this Note, we review the main existing results, methods, and some key open problems on the controllability of nonlinear hyperbolic and parabolic equations. Especially, we describe our recent universal approach to solve the local…
This paper considers a general framework for the study of the existence of quasi-variational and variational solutions to a class of nonlinear evolution systems in convex sets of Banach spaces describing constraints on a linear combination…
The purpose of this paper is to develop a numerical method for finding an equilibrium point in a model, in which the loss function of each object (subject) is described by a convex function with respect to one of its variables. Such models…
Vector optimization problems are a generalization of multiobjective optimization in which the preference order is related to an arbitrary closed and convex cone, rather than the nonnegative octant. Due to its real life applications, it is…
We study the existence and uniqueness of solutions to the inverse quasi-variational inequality problem. Motivated by the neural network approach to solving optimization problems such as variational inequality, monotone inclusion, and…
Equilibria of realistic multiplayer games constitute a key solution concept both in practical applications, such as online advertising auctions and electricity markets, and in analytical frameworks used to study strategic voting in…
We study turn-based quantitative multiplayer non zero-sum games played on finite graphs with reachability objectives. In such games, each player aims at reaching his own goal set of states as soon as possible. A previous work on this model…
We investigate a modular convex Nash equilibrium problem involving nonsmooth functions acting on linear mixtures of strategies, as well as smooth coupling functions. An asynchronous block-iterative decomposition method is proposed to solve…
Solution concepts such as Nash Equilibria, Correlated Equilibria, and Coarse Correlated Equilibria are useful components for many multiagent machine learning algorithms. Unfortunately, solving a normal-form game could take prohibitive or…
In this paper, we firstly prove the existence of the equilibrium for the generalized abstract economy. We apply these results to show the existence of solutions for systems of vector quasi-equilibrium problems with multivalued trifunctions.…
We address the generalized Nash equilibrium seeking problem in a partial-decision information scenario, where each agent can only exchange information with some neighbors, although its cost function possibly depends on the strategies of all…
We address the Nash equilibrium problem in a partial-decision information scenario, where each agent can only observe the actions of some neighbors, while its cost possibly depends on the strategies of other agents. Our main contribution is…
We study the extragradient method for solving vector quasi-equilibrium problems in Banach spaces, which generalizes the extragradient method for vector equilibrium problems and scalar quasi-equilibrium problems. We propose a regularization…
The preferences of players in non-cooperative games represent their choice in the set of available options, which meet the completeness property if players are able to compare any pair of available options. In the existing literature, the…
In this paper, we aim to design a distributed approximate algorithm for seeking Nash equilibria of an aggregative game. Due to the local set constraints of each player, projectionbased algorithms have been widely employed for solving such…
Quasi-equilibrium approximation is a widely used closure approximation approach for model reduction with applications in complex fluids, materials science, etc. It is based on the maximum entropy principle and leads to thermodynamically…
A \emph{new} notion of equilibrium, which we call \emph{strong equilibrium}, is introduced for time-inconsistent stopping problems in continuous time. Compared to the existing notions introduced in ArXiv: 1502.03998 and ArXiv: 1709.05181,…
The task of computing approximate Nash equilibria in large zero-sum extensive-form games has received a tremendous amount of attention due mainly to the Annual Computer Poker Competition. Immediately after its inception, two competing and…