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NASH EQUILIBRIUMS IN TWO-PERSON RED-AND-BLACK GAMES

Published online by Cambridge University Press:  08 June 2012

May-Ru Chen
May-Ru Chen
Affiliation:
National Sun Yat-sen University, Kaohsiung 80424, Taiwan, Republic of China E-mail: [email protected]
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Abstract

In a two-person red-and-black game, each player wants to maximize the probability of winning the entire fortune of his opponent by gambling repeatedly with suitably chosen stakes. We find the multiplicativity (including submultiplicative and supermultiplicative) of the win probability function is important for the profiles (bold, timid) or (bold, bold) to be a Nash equilibrium. Surprisingly, a Nash equilibrium condition for the profile (bold, any strategy) is also given in terms of multiplicativity. Finally, we search for some suitable conditions such that the profile (timid, timid) is also a Nash equilibrium.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 26 , Issue 3 , July 2012 , pp. 323 - 336
Copyright
Copyright © Cambridge University Press 2012

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