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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
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Abstract

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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, $n>2$

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 2 , June 2007 , pp. 547 - 553
Copyright
Copyright © Applied Probability Trust 2007 

References

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