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We study a new nonlinear system which contains a partial differential equation, a quasivariational inequality and a parabolic variational inequality in Banach spaces. We obtain the unique solvability of the coupled system under moderate…
We study an infinite-horizon discrete-time optimal stopping problem under non-exponential discounting. A new method, which we call the iterative approach, is developed to find subgame perfect Nash equilibria. When the discount function…
A class of quasilinear singularly perturbed boundary value problems with a turning point of attractive type is considered. The problems are solved numerically by a finite-difference scheme on a special discretization mesh which is dense…
We propose an augmented Lagrangian-type algorithm for the solution of generalized Nash equilibrium problems (GNEPs). Specifically, we discuss the convergence properties with regard to both feasibility and optimality of limit points. This is…
We prove the existence of solutions for an evolution quasi-variational inequality with a first order quasilinear operator and a variable convex set, which is characterized by a constraint on the absolute value of the gradient that depends…
Examining the behavior of multi-agent systems is vitally important to many emerging distributed applications - game theory has emerged as a powerful tool set in which to do so. The main approach of game-theoretic techniques is to model…
Establishing the existence of Nash equilibria for partially observed stochastic dynamic games is known to be quite challenging, with the difficulties stemming from the noisy nature of the measurements available to individual players…
We provide an in-depth study of Nash equilibria in multi-objective normal form games (MONFGs), i.e., normal form games with vectorial payoffs. Taking a utility-based approach, we assume that each player's utility can be modelled with a…
In dynamic games with shared constraints, Generalized Nash Equilibria (GNE) are often computed using the normalized solution concept, which assumes identical Lagrange multipliers for shared constraints across all players. While widely used,…
For any two-by-two game $\G$, we define a new two-player game $\G^Q$. The definition is motivated by a vision of players in game $\G$ communicating via quantum technology according to a certain standard protocol originally introduced by…
This article analyses the simple projection method proposed by Izuchukwu et al. [8, Algorithm 3.2] for solving variational inequality problems by incorporating momentum terms. A new step size strategy is also introduced, in which the step…
Using the simple case of Blasius similarity solution, we illustrate a recently developed general method that reduces a strongly nonlinear problem into a weakly nonlinear analysis. The basic idea is to find a quasi-solution $F_0$ that…
Motivated by Cournot models, this paper proposes novel models of the noncooperative and cooperative differential games with density constraints in infinite dimensions, where markets consist of infinite firms and demand dynamics are governed…
Nash equilibrium has long been a desired solution concept in multi-player games, especially for those on continuous strategy spaces, which have attracted a rapidly growing amount of interests due to advances in research applications such as…
This work gathers new results concerning the semi-geostrophic equations: existence and stability of measure valued solutions, existence and uniqueness of solutions under certain continuity conditions for the density, convergence to the…
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…
The concept of nonlinear split ordered variational inequality problems on partially ordered vector spaces is a natural extension of linear split vector variational inequality problems on Banach spaces. The results about nonlinear split…
In the context of large population symmetric games, approximate Nash equilibria are introduced through equilibrium solutions of the corresponding mean field game in the sense that the individual gain from optimal unilateral deviation under…
We prove three results on the existence and structure of Nash equilibria for quasisupermodular games. A theorem is purely order-theoretic, and the other two involve topological hypotheses. Our topological results genralize Zhou's theorem…
The paper proposes a novel hybrid method for solving equilibrium problems and fixed point problems. By constructing specially cutting-halfspaces, in this algorithm, only an optimization program is solved at each iteration without the…