On approximations of nonzero-sum uniformly continuous ergodic stochastic games

Andrzej Nowak

Applicationes Mathematicae (1999)

  • Volume: 26, Issue: 2, page 221-228
  • ISSN: 1233-7234

Abstract

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We consider a class of uniformly ergodic nonzero-sum stochastic games with the expected average payoff criterion, a separable metric state space and compact metric action spaces. We assume that the payoff and transition probability functions are uniformly continuous. Our aim is to prove the existence of stationary ε-equilibria for that class of ergodic stochastic games. This theorem extends to a much wider class of stochastic games a result proven recently by Bielecki [2].

How to cite

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Nowak, Andrzej. "On approximations of nonzero-sum uniformly continuous ergodic stochastic games." Applicationes Mathematicae 26.2 (1999): 221-228. <http://eudml.org/doc/219234>.

@article{Nowak1999,
abstract = {We consider a class of uniformly ergodic nonzero-sum stochastic games with the expected average payoff criterion, a separable metric state space and compact metric action spaces. We assume that the payoff and transition probability functions are uniformly continuous. Our aim is to prove the existence of stationary ε-equilibria for that class of ergodic stochastic games. This theorem extends to a much wider class of stochastic games a result proven recently by Bielecki [2].},
author = {Nowak, Andrzej},
journal = {Applicationes Mathematicae},
keywords = {Nash equilibrium; general state space; nonzero-sum Markov game; long run average reward criterion},
language = {eng},
number = {2},
pages = {221-228},
title = {On approximations of nonzero-sum uniformly continuous ergodic stochastic games},
url = {http://eudml.org/doc/219234},
volume = {26},
year = {1999},
}

TY - JOUR
AU - Nowak, Andrzej
TI - On approximations of nonzero-sum uniformly continuous ergodic stochastic games
JO - Applicationes Mathematicae
PY - 1999
VL - 26
IS - 2
SP - 221
EP - 228
AB - We consider a class of uniformly ergodic nonzero-sum stochastic games with the expected average payoff criterion, a separable metric state space and compact metric action spaces. We assume that the payoff and transition probability functions are uniformly continuous. Our aim is to prove the existence of stationary ε-equilibria for that class of ergodic stochastic games. This theorem extends to a much wider class of stochastic games a result proven recently by Bielecki [2].
LA - eng
KW - Nash equilibrium; general state space; nonzero-sum Markov game; long run average reward criterion
UR - http://eudml.org/doc/219234
ER -

References

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  1. [1] D. P. Bertsekas and S. E. Shreve, Stochastic Optimal Control: The Discrete Time Case, Academic Press, New York, 1979. Zbl0471.93002
  2. [2] T. R. Bielecki, Approximations of dynamic Nash games with general state and action spaces and ergodic costs for the players, Appl. Math. (Warsaw) 24 (1996), 195-202. Zbl0865.90146
  3. [3] E. B. Dynkin and A. A. Yushkevich, Controlled Markov Processes, Springer, New York, 1979. Zbl0073.34801
  4. [4] J. P. Georgin, Contrôle de chaînes de Markov sur des espaces arbitraires, Ann. Inst. H. Poincaré Sér. B 14 (1978), 255-277. Zbl0391.60066
  5. [5] O. Hernández-Lerma and J. B. Lasserre, Discrete Time Markov Control Pro- cesses: Basic Optimality Criteria, Springer, New York, 1996. 
  6. [6] S. P. Meyn and R. L. Tweedie, Markov Chains and Stochastic Stability, Springer, New York, 1993. Zbl0925.60001
  7. [7] S. P. Meyn and R. L. Tweedie, Computable bounds for geometric convergence rates of Markov chains, Ann. Appl. Probab. 4 (1994), 981-1011. Zbl0812.60059
  8. [8] J. Neveu, Mathematical Foundations of the Calculus of Probability, Holden-Day, San Francisco, 1965. Zbl0137.11301
  9. [9] A. S. Nowak, Existence of equilibrium stationary strategies in discounted noncooperative stochastic games with uncountable state space, J. Optim. Theory Appl. 45 (1985), 591-602. Zbl0543.90101
  10. [10] A. S. Nowak, A generalization of Ueno's inequality for n-step transition probabilities, Appl. Math. (Warsaw) 25 (1998), 295-299. Zbl0998.60068
  11. [11] A. S. Nowak and E. Altman, ε-Nash equilibria for stochastic games with uncountable state space and unbounded costs, technical report, Inst. Math., Wrocław Univ. of Technology, 1998 (submitted). 
  12. [12] A. S. Nowak and K. Szajowski, Nonzero-sum stochastic games, Ann. Dynamic Games 1999 (to appear). Zbl0940.91014
  13. [13] W. Whitt, Representation and approximation of noncooperative sequential games, SIAM J. Control Optim. 18 (1980), 33-48. Zbl0428.90094

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