Related papers: On asymptotic value for dynamic games with saddle …

The paper is concerned with two-person dynamic zero-sum games. We investigate the limit of value functions of finite horizon games with long run average cost as the time horizon tends to infinity, and the limit of value functions of…

For two-person dynamic zero-sum games (both discrete and continuous settings), we investigate the limit of value functions of finite horizon games with long run average cost as the time horizon tends to infinity and the limit of value…

This paper is concerned with two-person dynamic zero-sum games. Let games for some family have common dynamics, running costs and capabilities of players, and let these games differ in densities only. We show that the Dynamic Programming…

The paper is devoted to dynamic games. We consider a general enough framework, which is not limited to e.g. differential games and could accommodate both discrete and continuous time. Assuming common dynamics, we study two game families…

Bewley and Kohlberg (1976) and Mertens and Neyman (1981) have proved, respectively, the existence of the asymptotic value and the uniform value in zero-sum stochastic games with finite state space and finite action sets. In their work, the…

In \emph{zero-sum two-player hidden stochastic games}, players observe partial information about the state. We address: $(i)$ the existence of the \emph{uniform value}, i.e., a limiting average payoff that both players can guarantee for…

We consider two-player games played on weighted directed graphs with mean-payoff and total-payoff objectives, two classical quantitative objectives. While for single-dimensional games the complexity and memory bounds for both objectives…

We prove in a dynamic programming framework that uniform convergence of the finite horizon values implies that asymptotically the average accumulated payoff is constant on optimal trajectories. We analyze and discuss several possible…

This paper proves several Tauberian theorems for general iterations of operators, and provides two applications to zero-sum stochastic games where the total payoff is a weighted sum of the stage payoffs. The first application is to provide…

This paper concerns value functions of time-dependent tug-of-war games. We first prove the existence and uniqueness of value functions and verify that these game values satisfy a dynamic programming principle. Using the arguments in the…

Motivated by uncertain parameters encountered in Markov decision processes (MDPs) and stochastic games, we study the effect of parameter uncertainty on Bellman operator-based algorithms under a set-based framework. Specifically, we first…

In the paper we present a model of discrete-time mean-field game with several populations of players. Mean-field games with multiple populations of the players have only been studied in the literature in the continuous-time setting. The…

In several standard models of dynamic programming (gambling houses, MDPs, POMDPs), we prove the existence of a very robust notion of value for the infinitely repeated problem, namely the pathwise uniform value. This solves two open…

This paper considers continuously differentiable functions of two vector variables that have (possibly a continuum of) min-max saddle points. We study the asymptotic convergence properties of the associated saddle-point dynamics…

In this paper we study mean field games with possibly multiple mean field equilibria. Instead of focusing on the individual equilibria, we propose to study the set of values over all possible equilibria, which we call the set value of the…

This paper extends Berge's maximum theorem for possibly noncompact action sets and unbounded cost functions to minimax problems and studies applications of these extensions to two-player zero-sum games with possibly noncompact action sets…

We construct a statistical ensemble of games, where in each independent subensemble we have two players playing the same game. We derive the mean payoffs per move of the representative players of the game, and we evaluate all the…

We study the existence of different notions of value in two-person zero-sum repeated games where the state evolves and players receive signals. We provide some examples showing that the limsup value (and the uniform value) may not exist in…

The paper is devoted to the asymptotic behavior of value functions of abstract control problem with the long-time and discounted averages. The Uniform Tauberian Theorem for these problems states that the uniform convergence of value…

We consider a dynamic programming problem with arbitrary state space and bounded rewards. Is it possible to define in an unique way a limit value for the problem, where the "patience" of the decision-maker tends to infinity ? We consider,…