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On the Three-Person Game Baccara Banque

Author

Listed:
  • Stewart N. Ethier

    (Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, UT 84112, USA)

  • Jiyeon Lee

    (Department of Statistics, Yeungnam University, 214-1 Daedong, Kyeongsan, Kyeongbuk 712-749, South Korea)

Abstract

Baccara banque is a three-person zero-sum game parameterized by \(\theta\in(0,1)\). A study of the game by Downton and Lockwood claimed that the Nash equilibrium is of only academic interest. Their preferred alternative is what we call the independent cooperative equilibrium . However, this solution exists only for certain \(\theta\). A third solution, which we call the correlated cooperative equilibrium , always exists. Under a ''with replacement'' assumption as well as a simplifying assumption concerning the information available to one of the players, we derive each of the three solutions for all \(\theta\).

Suggested Citation

  • Stewart N. Ethier & Jiyeon Lee, 2015. "On the Three-Person Game Baccara Banque," Games, MDPI, vol. 6(2), pages 1-22, May.
    • Handle: RePEc:gam:jgames:v:6:y:2015:i:2:p:57-78:d:49324
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    References listed on IDEAS

    as
    1. N/A, 1968. "Gaming," Journal of Conflict Resolution, Peace Science Society (International), vol. 12(2), pages 222-223, June.
    2. N/A, 1968. "Gaming," Journal of Conflict Resolution, Peace Science Society (International), vol. 12(1), pages 82-82, March.
    3. Maschler,Michael & Solan,Eilon & Zamir,Shmuel, 2013. "Game Theory," Cambridge Books, Cambridge University Press, number 9781107005488.
    4. Stewart N. Ethier & Carlos Gámez, 2013. "A Game-Theoretic Analysis of Baccara Chemin de Fer," Games, MDPI, vol. 4(4), pages 1-27, November.
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    Cited by:

    1. Melkikh, A.V. & Beregov, R.Y. & Sutormina, M.I., 2022. "Strange attractors and nontrivial solutions in games with three players," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).

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