Related papers: Inverse initial problem under Nash strategy for st…
In this paper, we present a refined approach to establish a global Lipschitz stability for an inverse source problem concerning the determination of forcing terms in the wave equation with mixed boundary conditions. It consists of boundary…
Inverse problems aim to determine parameters from observations, a crucial task in engineering and science. Lately, generative models, especially diffusion models, have gained popularity in this area for their ability to produce realistic…
A moment constraint that limits the number of dividends in the optimal dividend problem is suggested. This leads to a new type of time-inconsistent stochastic impulse control problem. First, the optimal solution in the precommitment sense…
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…
We study stochastic Nash equilibrium problems subject to heterogeneous uncertainty on the expected valued cost functions of the individual agents, where we assume no prior knowledge of the underlying probability distributions of the…
Stochastic inverse problems considered in this article consist of estimating the probability distributions of intrinsically random inputs of computer models. These estimations are based on observable outputs affected by model noise, and…
This paper studies the inverse problem of determination the history for a stochastic diffusion process, by means of the value at the final time $T$. By establishing a new Carleman estimate, the conditional stability of the problem is…
In this paper, we address the challenge of Nash equilibrium (NE) seeking in non-cooperative convex games with partial-decision information. We propose a distributed algorithm, where each agent refines its strategy through projected-gradient…
In this paper, we consider two linear inverse problems for the time-fractional wave equation, assuming that its right-hand side takes the separable form $f(t)h(x)$, where $t \geq 0$ and $x \in \Omega \subset R^N $. The objective is to…
In this paper, we study a distributed continuous-time design for aggregative games with coupled constraints in order to seek the generalized Nash equilibrium by a group of agents via simple local information exchange. To solve the problem,…
We present a framework that incorporates the idea of bounded rationality into dynamic stochastic pursuit-evasion games. The solution of a stochastic game is characterized, in general, by its (Nash) equilibria in feedback form. However,…
We suggest a novel stochastic-approximation algorithm to compute a symmetric Nash-equilibrium strategy in a general queueing game with a finite action space. The algorithm involves a single simulation of the queueing process with dynamic…
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 reaction-diffusion equations with a stochastic perturbation on the boundary. We show that in the limit of fast diffusion, one can rigorously approximate solutions of the system of PDEs with stochastic Neumann boundary…
This paper considers a class of stochastic control problems with implicitly defined objective functions, which are the sources of time-inconsistency. We study the closed-loop equilibrium solutions in a general controlled diffusion…
We design a distributed algorithm to seek generalized Nash equilibria of a robust game with uncertain coupled constraints. Due to the uncertainty of parameters in set constraints, we aim to find a generalized Nash equilibrium in the worst…
Splitting methods constitute a well-established class of numerical schemes for solving convection-diffusion-reaction problems. They have been shown to be effective in solving problems with periodic boundary conditions. However, in the case…
This work considers stochastic differential games with a large number of players, whose costs and dynamics interact through the empirical distribution of both their states and their controls. We develop a new framework to prove convergence…
Many approaches to modelling reaction-diffusion systems with anomalous transport rely on deterministic equations and ignore fluctuations arising due to finite particle numbers. Starting from an individual-based model we use a…
A general topic of current interest is the analysis of diffusion problems in singularly perturbed domains with small interior targets or traps (the narrow capture problem). One major application is to intracellular diffusion, where the…