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2000 | 27 | 4 | 385-394
Tytuł artykułu

Some remarks on equilibria in semi-Markov games

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper is a first study of correlated equilibria in nonzero-sum semi-Markov stochastic games. We consider the expected average payoff criterion under a strong ergodicity assumption on the transition structure of the games. The main result is an extension of the correlated equilibrium theorem proven for discounted (discrete-time) Markov games in our joint paper with Raghavan. We also provide an existence result for stationary Nash equilibria in the limiting average payoff semi-Markov games with state independent and nonatomic transition probabilities. A similar result was proven for discounted Markov games by Parthasarathy and Sinha.
Rocznik
Tom
27
Numer
4
Strony
385-394
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-03-26
poprawiono
2000-03-30
Twórcy
  • Institute of Mathematics, Zielona Góra University of Technology, Podgórna 50, 65-246 Zielona Góra, Poland
Bibliografia
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  • [3] P. Billingsley, Probability and Measure, Wiley, New York, 1979.
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  • [5] N. Dunford and J. T. Schwartz, Linear Operators, Part 1: General Theory, Wiley-Interscience, New York, 1958.
  • [6] E. B. Dynkin and A. A. Yushkevich, Controlled Markov Processes, Springer, New York, 1979.
  • [7] F. Forges, An approach to communication equilibria, Econometrica 54 (1986), 1375-1385.
  • [8] I. L. Glicksberg, A further generalization of the Kakutani fixed point theorem with application to Nash equilibrium points, Proc. Amer. Math. Soc. 3 (1952), 170-174.
  • [9] H.-U. Küenle, Stochastic games with complete information and average cost criterion, in: Advances in Dynam. Games and Applications ( Kanagawa, 1996), Ann. Internat. Soc. Dynam. Games 5, Birkhäuser, Boston, 2000, 325-338.
  • [10] M. Kurano, Semi-Markov decision processes and their applications in replacement models, J. Oper. Res. Soc. Japan 28 (1985), 18-30.
  • [11] K. Kuratowski and C. Ryll-Nardzewski, A general theorem on selectors, Bull. Acad. Polon. Sci. 13 (1965), 397-403.
  • [12] H.-C. Lai and K. Tanaka, A noncooperative n-person semi-Markov game with a separable metric state space, Appl. Math. Optim. 11 (1984), 23-42.
  • [13] H.-C. Lai and K. Tanaka, On an n-person noncooperative Markov game with a metric state space, J. Math. Anal. Appl. 101 (1984), 78-96.
  • [14] A. K. Lal and S. Sinha, Zero-sum two-person semi-Markov games, J. Appl. Probab. 29 (1992), 56-72.
  • [15] J. Neveu, Mathematical Foundations of the Calculus of Probability, Holden-Day, San Francisco, 1965.
  • [16] A. S. Nowak, Stationary equilibria for nonzero-sum average payoff ergodic stochastic games with general state space, in: Advances in Dynamic Games and Applications, T. Basar and A. Haurie (eds.), Birkhäuser, New York, 1994, 231-246.
  • [17] A. S. Nowak, On approximations of nonzero-sum uniformly continuous ergodic stochastic games, Appl. Math. (Warsaw) 26 (1999), 221-228.
  • [18] A. S. Nowak and E. Altman, ε-Nash equilibria for stochastic games with uncountable state space and unbounded cost, technical report, Inst. Math., Wrocław Univ. of Technology, 1998.
  • [19] A. S. Nowak and T. E. S. Raghavan, Existence of stationary correlated equilibria with symmetric information for discounted stochastic games, Math. Oper. Res. 17 (1992), 519-526.
  • [20] A. S. Nowak and K. Szajowski, Nonzero-sum stochastic games, in: Stochastic and Differential Games, Ann. Internat. Soc. Dynam. Games 4, Birkhäuser, Boston, 1999, 297-342.
  • [21] T. Parthasarathy and S. Sinha, Existence of stationary equilibrium strategies in non-zero-sum discounted stochastic games with uncountable state space and state independent transitions, Internat. J. Game Theory 18 (1989), 189-194.
  • [22] W. Połowczuk, Nonzero-sum semi-Markov games with countable state spaces, this issue, 395-402.
  • [23] S. M. Ross, Applied Probability Models with Optimization Applications, Holden-Day, San Francisco, 1970.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-zmv27i4p385bwm
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