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Two-person red-and-black with bet-dependent win probabilities

Part of: Game theory

Published online by Cambridge University Press:  01 July 2016

Laura Pontiggia
Laura Pontiggia*
Affiliation:
University of Minnesota
*
∗ Postal address: School of Statistics, University of Minnesota, 313 Ford Hall, 224 Church Street SE, Minneapolis, MN 55455-0493, USA. Email address: pontla@stat.umn.edu
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Abstract

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We present two variations of a two-person, noncooperative stochastic game, inspired by the famous red-and-black gambling problem presented by Dubins and Savage. Two players each hold an integer amount of money and they each aim to win the other player's fortune. At every stage of the game they simultaneously bid an integer portion of their current fortune, and their probabilities of winning depend on these bids. We describe two different laws of motion specifying this dependency. In one version of the game, the players' probabilities of winning are proportional to their bets. In the other version, the probabilities of winning depend on the size of their bets and a weight parameter w. For each version we give a Nash equilibrium, in which the player for which the game is subfair (w ≤ ½) plays boldly and the player for which the game is superfair (w ≥ ½) plays timidly.

Keywords

Stochastic gamered-and-blackNash equilibrium

MSC classification

Primary: 91A15: Stochastic games
Secondary: 91A05: 2-person games
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 37 , Issue 1 , March 2005 , pp. 75 - 89
Copyright
Copyright © Applied Probability Trust 2005 

References

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