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We introduce an extended mathematical programming framework for specifying equilibrium problems and their variational representations, such as generalized Nash equilibrium, multiple optimization problems with equilibrium constraints, and…
We present a new methodology for computing approximate Nash equilibria for two-person non-cooperative games based upon certain extensions and specializations of an existing optimization approach previously used for the derivation of fixed…
In this paper, we propose two projection dynamical systems for solving inverse quasi-variational inequality problems in finite-dimensional Hilbert spaces-one ensuring finite-time stability and the other guaranteeing fixed-time stability. We…
We study the equilibrium problem on general Riemannian manifolds. The results on existence of solutions and on the convex structure of the solution set are established. Our approach consists in relating the equilibrium problem to a suitable…
Nash equilibria and Pareto optimality are two distinct concepts when dealing with multiple criteria. It is well known that the two concepts do not coincide. However, in this work we show that it is possible to characterize the set of all…
We show the validity of select existence results for a vector optimization problem, and a variational inequality. More generally, we consider generalized vector quasi-variational inequalities, as well as, fixed point problems on genuine…
We study quasi-convex optimization problems, where only a subset of the constraints can be sampled, and yet one would like a probabilistic guarantee on the obtained solution with respect to the initial (unknown) optimization problem. Even…
In this work, we present a novel characterization of approximate Nash equilibria in a class of convex games over the simplex. To achieve this, we regularize the utility functions using the Shannon entropy term, connect the solutions to the…
We consider a multi-agent noncooperative game with agents' objective functions being affected by uncertainty. Following a data driven paradigm, we represent uncertainty by means of scenarios and seek a robust Nash equilibrium solution. We…
This paper investigates the Nash equilibrium of a bi-objective optimal control problem governed by the Stokes equations. A multi-objective Nash strategy is formulated, and fundamental theoretical results are established, including the…
The equilibrium selection problem in the generalized Nash equilibrium problem (GNEP) has recently been studied as an optimization problem, defined over the set of all variational equilibria achievable through a lower-level non-cooperative…
Uniformly regular equilibrium problems are natural generalizations of abstract equilibrium prob lems and they are defined over the uniformly prox-regular nonconvex sets. Some new efficient implicit methods for solving uniformly regular…
Nash equilibrium is the most commonly-used notion of equilibrium in game theory. However, it suffers from numerous problems. Some are well known in the game theory community; for example, the Nash equilibrium of repeated prisoner's dilemma…
A new and simple method for quasi-convex optimization is introduced from which its various applications can be derived. Especially, a global optimum under constrains can be approximated for all continuous functions.
Adiabatic quantum computing is implemented on specialized hardware using the heuristics of the quantum annealing algorithm. This setup requires the addressed problems to be formatted as discrete quadratic functions without constraints and…
This work proposes a novel set of techniques for approximating a Nash equilibrium in a finite, normal-form game. It achieves this by constructing a new reformulation as solving a parameterized system of multivariate polynomials with tunable…
Recently, remarkable progress has been made by approximating Nash equilibrium (NE), correlated equilibrium (CE), and coarse correlated equilibrium (CCE) through function approximation that trains a neural network to predict equilibria from…
In this paper, we consider a new kind of evolution multivalued quasi-variational inequalities with feedback effect and a nonlinear bifunction which contain several (evolution) quasi-variational/hemivariational inequalities as special cases.…
This paper is focused on a stochastic quasi-variational inequality (SQVI) problem with a continuous and strongly-monotone mapping over a closed and convex set where the projection onto the constraint set may not be easy to compute. We…
In this paper, we consider some equilibrium problems (or saddle point problems), in which the domains of the considered mappings are limited at some regions. These restricted regions are defined by some mappings which are called the…