Related papers: Tauberian theorem for value functions

The paper investigates the long-time behavior of zero-sum linear-quadratic stochastic differential games, aiming to demonstrate that, under appropriate conditions, both the saddle strategy and the optimal state process exhibit the…

This paper presents new families of algorithms for the repeated play of two-agent (near) zero-sum games and two-agent zero-sum stochastic games. For example, the family includes fictitious play and its variants as members. Commonly, the…

We provide a deterministic-control-based interpretation for a broad class of fully nonlinear parabolic and elliptic PDEs with continuous Neumann boundary conditions in a smooth domain. We construct families of two-person games depending on…

Here, we study the existence and the convergence of solutions for the vanishing discount MFG problem with a quadratic Hamiltonian. We give conditions under which the discounted problem has a unique classical solution and prove convergence…

We study optimal control problems in infinite horizon when the dynamics belong to a specific class of piecewise deterministic Markov processes constrained to star-shaped networks (inspired by traffic models). We adapt the results in [H. M.…

We study a class of stochastic target games where one player tries to find a strategy such that the state process almost-surely reaches a given target, no matter which action is chosen by the opponent. Our main result is a geometric dynamic…

Simple stochastic games can be solved by value iteration (VI), which yields a sequence of under-approximations of the value of the game. This sequence is guaranteed to converge to the value only in the limit. Since no stopping criterion is…

In this paper we find viscosity solutions to the two membranes problem (that is a system with two obstacle-type equations) with two different $p-$Laplacian operators taking limits of value functions of a sequence of games. We analyze…

In this paper the set of value functions of all-possible zero-sum differential games with terminal payoff is characterized. The necessary and sufficient condition for a given function to be a value of some differential game with terminal…

The remarkable success of the Adam in training neural networks has naturally led to the widespread use of its descent-ascent counterpart, Adam-DA, for solving zero-sum games. Despite its popularity in practice, a rigorous theoretical…

We consider two person zero-sum games where the players control, at discrete times {tn} induced by a partition $\Pi$ of R + , a continuous time Markov state process. We prove that the limit of the values v$\Pi$ exist as the mesh of $\Pi$…

In this work, we investigate a security game between an attacker and a defender, originally proposed in \cite{emadi2019security}. As is well known, the combinatorial nature of security games leads to a large cost matrix. Therefore,…

This paper considers discounted infinite horizon mean field games by extending the probabilistic weak formulation of the game as introduced by Carmona and Lacker (2015). Under similar assumptions as in the finite horizon game, we prove…

We introduce the notion of universal graphs as a tool for constructing algorithms solving games of infinite duration such as parity games and mean payoff games. In the first part we develop the theory of universal graphs, with two goals:…

The hybrid optimal control problem with reach time to a target set is addressed and the continuity and uniqueness of the associated value function is proved. Hybrid systems involves interaction of different types of dynamics: continuous and…

In the present work, we consider 2-person zero-sum stochastic differential games with a nonlinear pay-off functional which is defined through a backward stochastic differential equation. Our main objective is to study for such a game the…

This paper uses recent results on continuous-time finite-horizon optimal switching problems with negative switching costs to prove the existence of a saddle point in an optimal stopping (Dynkin) game. Sufficient conditions for the game's…

We introduce novel multi-agent interaction models of entropic spatially inhomogeneous evolutionary undisclosed games and their quasi-static limits. These evolutions vastly generalize first and second order dynamics. Besides the…

We establish existence of nearly-optimal controls, conditions for existence of an optimal control and a saddle-point for respectively a control problem and zero-sum differential game associated with payoff functionals of mean-field type,…

This paper addresses the problem of utility maximization under uncertain parameters. In contrast with the classical approach, where the parameters of the model evolve freely within a given range, we constrain them via a penalty function. We…