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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…
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 examines finite zero-sum stochastic games and demonstrates that when the game's duration is sufficiently long, there exists a pair of approximately optimal strategies such that the expected average payoff at any point in the game…
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…
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…
The paper is concerned with two-person games with saddle point. We investigate the limits of value functions for long-time-average payoff, discounted average payoff, and the payoff that follows a probability density. Most of our assumptions…
We consider dynamic programming problems with a large time horizon, and give sufficient conditions for the existence of the uniform value. As a consequence, we obtain an existence result when the state space is precompact, payoffs are…
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…
Pursuit-evasion scenarios appear widely in robotics, security domains, and many other real-world situations. We focus on two-player pursuit-evasion games with concurrent moves, infinite horizon, and discounted rewards. We assume that the…
We consider integer-valued random walks with independent but not identically distributed increments, and extend to this context several classical estimates, including a local limit theorem, precise small-ball estimates (both conditional on…
We study the infinite-horizon restless bandit problem with the average reward criterion, in both discrete-time and continuous-time settings. A fundamental goal is to efficiently compute policies that achieve a diminishing optimality gap as…
We analyze Receding Horizon Games without any MPC-like terminal ingredients. We show that recursive feasibility can be inferred from the turnpike phenomenon under mild assumptions. Moreover, we prove sufficient conditions for practical…
We consider the infinite-horizon, average-reward restless bandit problem in discrete time. We propose a new class of policies that are designed to drive a progressively larger subset of arms toward the optimal distribution. We show that our…
We study the ergodicity of deterministic two-person zero-sum differential games. This property is defined by the uniform convergence to a constant of either the infinite-horizon discounted value as the discount factor tends to zero, or…
This paper studies a discrete-time optimal switching problem on a finite horizon. The underlying model has a running reward, terminal reward and signed (positive and negative) switching costs. Using the martingale approach to optimal…
We conduct a comprehensive analysis of the discrete-time exponential-weights dynamic with a constant step size on all general-sum and symmetric $2 \times 2$ normal-form games, i.e. games with $2$ pure strategies per player, and where the…
This paper aims to solve two fundamental problems on finite or infinite horizon dynamic games with perfect or almost perfect information. Under some mild conditions, we prove (1) the existence of subgame-perfect equilibria in general…
We study two-player zero-sum stopping games in continuous time and infinite horizon. We prove that the value in randomized stopping times exists as soon as the payoff processes are right-continuous. In particular, as opposed to existing…
Pursuit-Evasion Games (in discrete time) are stochastic games with nonnegative daily payoffs, with the final payoff being the cumulative sum of payoffs during the game. We show that such games admit a value even in the presence of…
This paper extends the core results of discrete time infinite horizon dynamic programming to the case of state-dependent discounting. We obtain a condition on the discount factor process under which all of the standard optimality results…