Stochastic differential games: Occupation measure based approach

  • V. S. Borkar
  • M. K. Ghosh
Contributed Papers

Abstract

A new approach based on occupation measures is introduced for studying stochastic differential games. For two-person zero-sum games, the existence of values and optimal strategies for both players is established for various payoff criteria. ForN-person games, the existence of equilibria in Markov strategies is established for various cases.

Key Words

Occupation measure Markov strategy invariant measure Isaacs equation equilibrium 

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References

  1. 1.
    Elliott, R. J., andDavis, M. H. A.,Optimal Play in a Stochastic Differential Game, SIAM Journal on Control and Optimization, Vol. 19, pp. 543–554, 1981.Google Scholar
  2. 2.
    Varaiya, P. P.,N-Player Stochastic Differential Games, SIAM Journal on Control and Optimization, Vol. 14, pp. 538–545, 1976.Google Scholar
  3. 3.
    Uchida, K.,On Existence of a Nash Equilibrium Point in N-Person Nonzero-Sum Stochastic Differential Games, SIAM Journal on Control and Optimization, Vol. 16, pp. 142–149, 1978.Google Scholar
  4. 4.
    Uchida, K.,A Note on the Existence of a Nash Equilibrium Point in Stochastic Differential Games, SIAM Journal on Control and Optimization, Vol. 17, pp. 1–3, 1979.Google Scholar
  5. 5.
    Borkar, V. S.,Optimal Control of Diffusion Processes, Longman Scientific and Technical, Harlow, England, 1989.Google Scholar
  6. 6.
    Veretennikov, A. Ju.,On Strong Solution and Explicit Formulas for Solutions of Stochastic Integral Equations, Mathematics of the USSR-Sbornik, Vol. 39, pp. 387–403, 1981.Google Scholar
  7. 7.
    Bhattacharya, R. N.,Asymptotic Behavior of Several Dimensional Diffusions, Stochastic Nonlinear Systems, Edited by L. Arnold and R. Lefever, Springer-Verlag, New York, New York, pp. 86–99, 1981.Google Scholar
  8. 8.
    Krylov, N. V.,Controlled Diffusion Processes, Springer-Verlag, New York, New York, 1980.Google Scholar
  9. 9.
    Borkar, V. S., andGhosh, M. K.,Controlled Diffusion with Constraints, Journal of Mathematical Analysis and Applications, Vol. 152, pp. 88–108, 1990.Google Scholar
  10. 10.
    Aronson, D. G.,Bounds for the Fundamental Solution of a Parabolic Equation, Bulletin of the American Mathematical Society, Vol. 73, pp. 890–896, 1967.Google Scholar
  11. 11.
    Ladyzenskaya, O. A., Solonnikov, V. A., andUral'ceva, N. N.,Linear and Quasilinear Equations of Parabolic Type, American Mathematical Society, Providence, Rhode Island, 1968.Google Scholar
  12. 12.
    Fan, K.,Fixed Point and Minimax Theorems in Locally Convex Topological Linear Spaces, Proceedings of the National Academy of Sciences, USA, Vol. 38, pp. 121–126, 1952.Google Scholar
  13. 13.
    Grisvard, P.,Elliptic Problems in Nonsmooth Domains, Pitman, Boston, Massachusetts, 1965.Google Scholar
  14. 14.
    Beneš, V. E.,Existence of Optimal Strategies Based on a Specified Information, for a Class of Stochastic Decision Problems, SIAM Journal on Control and Optimization, Vol. 8, pp. 179–188, 1970.Google Scholar

Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • V. S. Borkar
    • 1
  • M. K. Ghosh
    • 2
  1. 1.Department of Electrical EngineeringIndian Institute of ScienceBangaloreIndia
  2. 2.Tata Institute of Fundamental ResearchBangaloreIndia

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