Hostname: page-component-76fb5796d-dfsvx Total loading time: 0 Render date: 2024-04-26T14:31:55.150Z Has data issue: false hasContentIssue false
  • English
  • Français

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: mayru@faculty.nsysu.edu.tw
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Chen, M.-R. (2009). Proportional three-person red-and-black games. Probability in the Engineering and Informational Sciences 23: 37–50.CrossRefGoogle Scholar
2.Chen, M.-R. (2011). Two-person red-and-black game with lower limit. Probability in the Engineering and Informational Sciences 25: 119–133.CrossRefGoogle Scholar
3.Chen, M.-R. & Hsiau, S.-R. (2006). Two-person red-and-black games with bet-dependent win probability functions. Journal of Applied Probability 43: 905–915.CrossRefGoogle Scholar
4.Chen, M.-R. & Hsiau, S.-R. (2010). Two new models of two-person red-and-black game. Journal of Applied Probability 47: 97–108.CrossRefGoogle Scholar
5.Dubins, L.E. & Savage, L.J. (1976). Inequalities for stochastic processes: How to gamble if you must, 2nd ed.New York: Dover.Google Scholar
6.Maitra, A.P. & Sudderth, W.D. (1996). Discrete gambling and stochastic games. New York: Springer-Verlag.CrossRefGoogle Scholar
7.Pontiggia, L. (2005). Two-person red-and-black with bet-dependent win probability. Advances in Applied Probability 37: 75–89.CrossRefGoogle Scholar
8.Pontiggia, L. (2007). Nonconstant sum red-and-black games with bet-dependent win probability function. Journal of Applied Probability 44: 547–553.CrossRefGoogle Scholar
9.Ross, S.M. (1974). Dynamic programming and gambling models. Advances in Applied Probability 6: 598–606.CrossRefGoogle Scholar
10.Secchi, P. (1997). Two-person red-and-black stochastic games. Journal of Applied Probability 34: 107–126.CrossRefGoogle Scholar