Skip to main content
SpringerLink
Log in

Juegos estocasticos continuos: Valor y estrategias optimas

  • Published:
Trabajos de Investigacion Operativa

Resumen

El objeto de este trabajo es analizar los juegos estocásticos cuyo espacio de estados y de acciones son métricos compactos, con adecuadas condiciones de continuidad acerca de las funciones de pago y de transición. Tras describir el modelo e introducir las hipótesis de continuidad, se trata el problema con horizonte finito, a fin de probar que existe valor y estrategias óptimas para ambos jugadores, que pueden ser determinados recurrentemente. También se considera el caso de horizonte infinito en presencia de un factor de descuento. El resultado final, en este caso, fue obtenido en Maitra-Parthasarathy (1970) mediante una demostración considerablemente más complicada. La simplificación se basa en la introducción de un pago terminal, que puede ser adecuadamente elegido a fin de obtener las conclusiones deseadas.

Abstract

The aim of this paper is to analyse stochastic games with state and action spaces wich are metric and compact and with suitable continuity conditions about the payoff and transition functions. After the description of the model and the introduction of the continuity assumptions, the finite horizon problem is analyzed, in order to prove that a value exists and both players have optimal strategies, that can be recursively determined. The discounted infinite horizon case is also considered. The final result in this case was obtained in Maitra-Parthasarathy (1970) with a considerably more cumbersome proof. The simplification is based in the introduction of a terminal payoff, that can be suitably choosed in order to get the desired conclusions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Referencias

  • BEWLEY, T., y KOHLBERG, E. (1976a): «The asymtotic theory of stochastic games»,Math. of O. R., vol. 1, 197–208.

    MATH  MathSciNet  Google Scholar 

  • BEWLEY, T., y KOHLBERG, E. (1976b): «The asymtotic solution of a recursive equation arising in stochastic games»,Math. of O. R., vol. 1, 321–336.

    MATH  MathSciNet  Google Scholar 

  • BEWLEY, T., y KOHLBERG, E. (1978): «On stochastic games with stationary optimal strategies»,Math. of O. R., vol. 3, 104–125.

    Article  MATH  MathSciNet  Google Scholar 

  • DUBINS, L. E., y SAVAGE, L. J. (1965):How to gamble in you must, McGraw-Hill Book Company, New York.

    Google Scholar 

  • GILLETTE, D. (1957): «Stochastic games with zero stop probabilities», en: Dresher, M., A. W. Tucker y P. Wolfe (eds.),Contributions to the theory of games, vol. III,Ann. of Math. Stud., 39, Princeton Univ. Press, Princeton.

    Google Scholar 

  • GROENEWEGEN, L., y WESSELS, J. (1976):On the relation between optimality and saddle-conservation in Markov games, Eindhoven Univ. of Technology, Dep. of Math., Memorandum COSOR, 76-14.

  • HOFFMAN, A., y KARP, R. (1966): «On nonterminating stochastic games»,Man. Science, vol. 12, 359–370.

    MathSciNet  Google Scholar 

  • KUSHNER, H. J., y CHAMBERLAIN, S. G. (1969):Finite state stochastic games: existence theorems and computational procedures, IEEE, Trans Automatic Control, AC-14, 248–255.

    Article  MathSciNet  Google Scholar 

  • MAITRA, A., y PARTHASARATHY, T. (1970): «On stochastic games»,J.O.T.A., vol. 5, 289–300.

    Article  MATH  MathSciNet  Google Scholar 

  • MAITRA, A., y PARTHASARATHY, T. (1970): «On stochastic games II»,J.O.T.A., vol. 8, 154–160.

    Article  MathSciNet  Google Scholar 

  • MERTENS, J. F., NEYMAN, A. (1981): «Stochastic games»,Int. J. of Game Theory, vol. 10, 53–56.

    Article  MATH  MathSciNet  Google Scholar 

  • MONASH, C. A. (1979):Stochastic games: The minmax theorem, Thesis submitted to the dep. of Math. of the Harvard Univ., Cambridge, Massachusetts.

  • PARTHASARATHY, T. (1971): «Discounted and positive stochastic games»,Bull. Amer. Math. Soc., vol. 77, 134–136.

    Article  MATH  MathSciNet  Google Scholar 

  • PARTHASARATHY, T., y RAGHAVAN, T. E. S. (1981): «An orderfield property for stochastic games when one player controls transition probabilities»,J.O.T.A., vol. 33, 375–392.

    Article  MATH  MathSciNet  Google Scholar 

  • ROGERS, P. D. (1969):Non-zero-sum stochastic games, Ph. D. Dissertation, Report ORC 69-8, Operations Research Centre, Univ. of California, Berkeley.

    Google Scholar 

  • SHAPLEY, L. S. (1953): «Stochastic games»,Proc. Nat. Acad. Sci. U.S.A., vol. 39, 1095–1100.

    Article  MATH  MathSciNet  Google Scholar 

  • STERN, M. A. (1975):On stochastic games with limiting average payoff, Ph. D. Dissertation, Univ. of Illinois, Chicago.

    Google Scholar 

  • WESSELS, J. (1977): «Markov games with unbounded rewards», en: M. Schäl,Dynamische optimierung, Bonner Mathematische Schriften, n.o 98.

Download references

Authors
  1. M. Angeles Muruaga
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Vélez Uned
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Muruaga, M.A., Uned, R.V. Juegos estocasticos continuos: Valor y estrategias optimas. Trabajos de Investigacion Operativa 7, 63–76 (1992). https://doi.org/10.1007/BF02888257

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02888257

Key words

AMS 1980-Subject Classification

Search

Navigation