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.
Publisher
Cambridge University Press (CUP)
Subject
Industrial and Manufacturing Engineering,Management Science and Operations Research,Statistics, Probability and Uncertainty,Statistics and Probability