Journal ArticleDOI
Optimal strategies in a class of zero-sum ergodic stochastic games
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Under such assumptions and some regularity conditions on the primitive data, it is proved the existence of optimal stationary strategies for the players in the expected average payoff stochastic games.Abstract:
In this paper we study zero-sum stochastic games with Borel state spaces. We make some stochastic stability assumptions on the transition structure of the game which imply the so-called w-uniform geometric ergodicity of Markov chains induced by stationary strategies of the players. Under such assumptions and some regularity conditions on the primitive data, we prove the existence of optimal stationary strategies for the players in the expected average payoff stochastic games. We also provide a first result on overtaking optimality in zero-sum stochastic games.read more
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Book ChapterDOI
Nonzero-sum Stochastic Games
TL;DR: In this article, a survey of stochastic Markov games with general state spaces is presented. But the authors focus on nonzero-sum games and provide a detailed survey of selected recent results.
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Minimax Control of Discrete-Time Stochastic Systems
TL;DR: A unified, self-contained presentation of minimax control problems for discrete-time stochastic systems on Borel spaces, with possibly unbounded costs, specialized to control systems with unknown disturbance distributions.
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The average cost optimality equation: A fixed point approach
TL;DR: In this paper, the expected average cost optimal control problem for discrete-time Markov control processes with Borel spaces and possibly unbounded costs was studied and the existence of an stationary optimal policy was shown under a Lyapunov stability condition and a growth condition on the costs.
Journal ArticleDOI
Zero-Sum Ergodic Stochastic Games with Feller Transition Probabilities
Anna Jaśkiewicz,Andrzej S. Nowak +1 more
TL;DR: The main objective of this paper is to establish a minimax theorem for a class of ergodic stochastic games with the Feller transition probability function with a generalized geometric ergodicity condition.
Journal ArticleDOI
Zero-sum stochastic games in borel spaces: average payoff criteria ∗
TL;DR: Conditions under which the long-run expected average payoff criterion, the sample-path average criterion,The existence of solutions to the average payoff Shapley equations, and a certain "martingale condition" are all equivalent are given.
References
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Book
Markov Chains and Stochastic Stability
Sean P. Meyn,Richard L. Tweedie +1 more
TL;DR: This second edition reflects the same discipline and style that marked out the original and helped it to become a classic: proofs are rigorous and concise, the range of applications is broad and knowledgeable, and key ideas are accessible to practitioners with limited mathematical background.
Journal ArticleDOI
The mathematical theory of saving
TL;DR: JSTOR transmission may be copied, downloaded,stored, further transmitted, transferred, distributed, altered, or otherwise used, in any form or by any means, except: (1) one stored electronic and one paper copy of any article solely for personal, non-commercial use, or (2) with prior written permission of JSTOR and the publisher of the article or other text.
Journal ArticleDOI
Stochastic Games
TL;DR: In a stochastic game the play proceeds by steps from position to position, according to transition probabilities controlled jointly by the two players, and the expected total gain or loss is bounded by M, which depends on N 2 + N matrices.
Book
Stochastic optimal control : the discrete time case
TL;DR: This research monograph is the authoritative and comprehensive treatment of the mathematical foundations of stochastic optimal control of discrete-time systems, including thetreatment of the intricate measure-theoretic issues.
Journal ArticleDOI
Minimax Theorems
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