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Antagonistic Game with Interval Payoff Functions

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Abstract

A two-person zero sum noncooperative game with an interval uncertain strategy and a payoff function is considered. With the use of methods of an extended interval arithmetic, external estimates are obtained for generalized sets of lower and upper values of the game defined by an interval payoff matrix.

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REFERENCES

  1. E. S. Ventsel', Operations Research [in Russian], Sov. Radio, Moscow (1972).

    Google Scholar 

  2. E. Quade, Analysis of Complex Systems [Russian translation], Sov. Radio, Moscow (1969).

    Google Scholar 

  3. O. I. Larichev and E. M. Moshkovich, Qualitative Methods in Decision-Making [in Russian], Nauka, Moscow (1996).

    Google Scholar 

  4. J. von Neumann and O. Morgenstern, The Theory of Games and Economic Behaviour, John Wiley and Sons (1944).

  5. P.C. Fishburn, Utility Theory for Decision Making, Wiley and Sons, (1970).

  6. A. Kofman, Introduction to the Theory of Fuzzy Sets [in Russian], Radio i Svyaz', Moscow (1992).

    Google Scholar 

  7. S. A. Kalmykov, Yu. I. Shokin, and Z. H. Yuldashev, Methods of the Interval Analysis [in Russian], Nauka, Novosibirsk (1986).

    Google Scholar 

  8. A. V. Lakeev and S. I. Noskov, “About the set of solutions of a linear equation with interval operator and right-hand side,” Sib. Mat. Zhurn., 35, No. 5, 1074–1084 (1994).

    Google Scholar 

  9. E. Kaucher, “Interval analysis in the extended interval space IR,” Comp. Suppl., No. 2, 33–49 (1980).

    Google Scholar 

  10. S. P. Sharyi, “The algebraic approach to the analysis of linear statistical systems with interval indeterminacy,” Izv. RAN, Theory and Control Systems, No. 3, 51–61 (1997).

    Google Scholar 

  11. L. A. Petrosyan, N. A. Zenkevich, and E. A. Semina, The Game Theory [in Russian], Vyssh. Shk., Moscow (1998).

    Google Scholar 

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Authors and Affiliations

  1. State Polytechnic University, St.-Petersburg, Russia

    V. N. Shashikhin

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  1. V. N. Shashikhin
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Shashikhin, V.N. Antagonistic Game with Interval Payoff Functions. Cybernetics and Systems Analysis 40, 556–564 (2004). https://doi.org/10.1023/B:CASA.0000047877.10921.d0

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  • DOI: https://doi.org/10.1023/B:CASA.0000047877.10921.d0

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