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Continuity of equilibria for two-person zero-sum games with noncompact action sets and unbounded payoffs

Author

Listed:
  • Eugene A. Feinberg

    (Stony Brook University)

  • Pavlo O. Kasyanov

    (National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”)

  • Michael Z. Zgurovsky

    (National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”)

Abstract

This paper extends Berge’s maximum theorem for possibly noncompact action sets and unbounded cost functions to minimax problems and studies applications of these extensions to two-player zero-sum games with possibly noncompact action sets and unbounded payoffs. For games with perfect information, also known under the name of turn-based games, this paper establishes continuity properties of value functions and solution multifunctions. For games with simultaneous moves, it provides results on the existence of lopsided values (the values in the asymmetric form) and solutions. This paper also establishes continuity properties of the lopsided values and solution multifunctions.

Suggested Citation

  • Eugene A. Feinberg & Pavlo O. Kasyanov & Michael Z. Zgurovsky, 2022. "Continuity of equilibria for two-person zero-sum games with noncompact action sets and unbounded payoffs," Annals of Operations Research, Springer, vol. 317(2), pages 537-568, October.
    • Handle: RePEc:spr:annopr:v:317:y:2022:i:2:d:10.1007_s10479-017-2677-y
    DOI: 10.1007/s10479-017-2677-y
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    References listed on IDEAS

    as
    1. Anna Jaśkiewicz & Andrzej Nowak, 2011. "Stochastic Games with Unbounded Payoffs: Applications to Robust Control in Economics," Dynamic Games and Applications, Springer, vol. 1(2), pages 253-279, June.
    2. Eugene A. Feinberg & Pavlo O. Kasyanov & Nina V. Zadoianchuk, 2012. "Average Cost Markov Decision Processes with Weakly Continuous Transition Probabilities," Mathematics of Operations Research, INFORMS, vol. 37(4), pages 591-607, November.
    3. Eugene A. Feinberg & Pavlo O. Kasyanov & Michael Z. Zgurovsky, 2016. "Partially Observable Total-Cost Markov Decision Processes with Weakly Continuous Transition Probabilities," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 656-681, May.
    4. Junmin Shi & Michael Katehakis & Benjamin Melamed, 2013. "Martingale methods for pricing inventory penalties under continuous replenishment and compound renewal demands," Annals of Operations Research, Springer, vol. 208(1), pages 593-612, September.
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