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Methods for Matrix Games with Mixed Strategies and Quantile Payoff Function

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Mathematical Optimization Theory and Operations Research (MOTOR 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1090))

Abstract

Walsh–Vries approach to matrix games with mixed strategies is considered. According to this approach, the payment function is defined not as the mathematical expectation of a random gain in a long series of parties, but as its quantile (VaR-estimate) for a given level of risk. The properties of such games are studied, and the methods for their solution are suggested.

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References

  1. Von Neumann, J., Morgenstern, O.: The Theory of Games and Economic Behavior. Princeton University Press, Princeton (1944)

    Google Scholar 

  2. Karlin, S.: Mathematical Methods in Games, Programming and Economics. In two vols. Dover Publications Inc., New York (1959). Reprinted 1992

    Google Scholar 

  3. Luce, R.D., Raiffa, H.: Games and Decisions. Introduction and Critical Survey. Dover Publication Inc., New York (1957). Reprinted 1989

    Google Scholar 

  4. Walsh, J.E.: Discrete two-person game theory with median payoff criterion. Opsearch (J. Oper. Res. Soc. India) 6(2), 83–97 (1969)

    Google Scholar 

  5. Walsh, J.E., Kelleher, G.J.: Generally applicable two-person percentile game theory. Opsearch (J. Oper. Res. Soc. India) 8(2), 143–152 (1971)

    Google Scholar 

  6. De Vries, H.: Quantile criteria for the selection of strategies in game theory. Int. J. Game Theory 3(2), 105–114 (1974)

    Article  MathSciNet  Google Scholar 

  7. Kibzun, A.I., Kan, Y.S.: Stochastic Programming Problems with Probability and Quantile Functions. Wiley, Chichester (1996)

    MATH  Google Scholar 

  8. Uryasev, S., Rockafellar, R.T.: Conditional value-at-risk: optimization approach. In: Uryasev, S., Pardalos, P.M. (Eds.) Stochastic Optimization: Algorithms and Applications, pp. 411–435. Kluwer, London (2001)

    MATH  Google Scholar 

  9. Kan, Y.S., Krasnopol’skaya, A.N.: Selection of a fixed-income portfolio. Autom. Remote Control 67(4), 598–605 (2006). https://doi.org/10.1134/S0005117906040072

    Article  MathSciNet  MATH  Google Scholar 

  10. Pankov, A.R., Platonov, E.N., Semenikhin, K.V.: Minimax optimization of investment portfolio by quantile criterion. Autom. Remote Control 64(7), 1122–1137 (2003)

    Article  MathSciNet  Google Scholar 

  11. Konyukhovskiy, P.V., Malova, A.S.: Game-theoretic models of collaboration among economic agents. Contrib. Game Theory Manage. 6, 211–221 (2013)

    MathSciNet  MATH  Google Scholar 

  12. Murtagh, B.: Advanced Linear Programming: Computation and Practice. MacGraw-Hill Intern., New York (1981)

    MATH  Google Scholar 

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Correspondence to Leonid D. Popov .

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Popov, L.D. (2019). Methods for Matrix Games with Mixed Strategies and Quantile Payoff Function. In: Bykadorov, I., Strusevich, V., Tchemisova, T. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2019. Communications in Computer and Information Science, vol 1090. Springer, Cham. https://doi.org/10.1007/978-3-030-33394-2_24

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  • DOI: https://doi.org/10.1007/978-3-030-33394-2_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-33393-5

  • Online ISBN: 978-3-030-33394-2

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