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Games 2015, 6(2), 57-78; doi:10.3390/g6020057

On the Three-Person Game Baccara Banque

1
Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, UT 84112, USA
2
Department of Statistics, Yeungnam University, 214-1 Daedong, Kyeongsan, Kyeongbuk 712-749, South Korea
*
Author to whom correspondence should be addressed.
Academic Editor: Erik Balder
Received: 24 November 2014 / Revised: 14 April 2015 / Accepted: 30 April 2015 / Published: 8 May 2015
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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 \(\theta\). View Full-Text
Keywords: baccara banque; baccara à deux tableaux; three-person game; sampling with replacement; Nash equilibrium; independent cooperative equilibrium; correlated cooperative equilibrium baccara banque; baccara à deux tableaux; three-person game; sampling with replacement; Nash equilibrium; independent cooperative equilibrium; correlated cooperative equilibrium
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Ethier, S.N.; Lee, J. On the Three-Person Game Baccara Banque. Games 2015, 6, 57-78.

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