Hostname: page-component-77c89778f8-gq7q9 Total loading time: 0 Render date: 2024-07-17T01:58:21.743Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonconstant Sum Red-And-Black Games with Bet-Dependent Win Probability Function

Part of: Game theory

Published online by Cambridge University Press:  14 July 2016

Laura Pontiggia
Laura Pontiggia*
Affiliation:
University of the Sciences in Philadelphia
*
∗ Postal address: Department of Mathematics, Physics and Computer Science, University of the Sciences in Philadelphia, 600 South 43rd Street, Philadelphia, PA 19104, USA. Email address: l.pontig@usip.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we investigate a class of N-person nonconstant sum red-and-black games with bet-dependent win probability functions. We assume that N players and a gambling house are engaged in a game played in stages, where the player's probability of winning at each stage is a function f of the ratio of his bet to the sum of all the players' bets. However, at each stage of the game there is a positive probability that all the players lose and the gambling house wins their bets. We prove that if the win probability function is super-additive and it satisfies f(s)f(t)≤f(st), then a bold strategy is optimal for all players.

Keywords

Stochastic gamesnonconstant sum gamesred-and-black

MSC classification

Primary: 91A15: Stochastic games
Secondary: 91A05: 2-person games 91A06: $n$-person games, $n>2$
Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 2 , June 2007 , pp. 547 - 553
Copyright
Copyright © Applied Probability Trust 2007 

References

Chen, M. and Hsiau, S. (2006). Two-person red-and-black games with bet-dependent win probability functions. J. Appl. Prob. 43, 905–915.Google Scholar
Dubins, L. and Savage, L. (1976). Inequalities for Stochastic Processes: How to Gamble if You Must, 2nd edn. Dover, New York.Google Scholar
Maitra, A. P. and Sudderth, W. D. (1996). Discrete Gambling and Stochastic Games. Springer, New York.Google Scholar
Pontiggia, L. (2005). Two-person red-and-black with bet-dependent win probabilities. Adv. Appl. Prob. 37, 75–89.CrossRefGoogle Scholar
Ross, S. M. (1974). Dynamic programming and gambling models. Adv. Appl. Prob. 6, 598–606.CrossRefGoogle Scholar