Two-person red-and-black games with bet-dependent win probability functions

May Ru Chen, Shoou Ren Hsiau

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

In this paper a two-person red-and-black game is investigated. We suppose that, at every stage of the game, player I's win probability, f, is a function of the ratio of his bet to the sum of both players' bets. Two results are given: (i) if f is convex then a bold strategy is optimal for player I when player II plays timidly; and (ii) if f satisfies f(s)f(t) ≤ f(st) then a timid strategy is optimal for player II when player I plays boldly. These two results extend two formulations of red-and-black games proposed by Pontiggia (2005), and also provide a sufficient condition to ensure that the profile (bold, timid) is the unique Nash equilibrium for players I and II. Finally, we give a counterexample to Pontiggia's conjecture about a proportional N-person red-and-black game.

Original languageEnglish
Pages (from-to)905-915
Number of pages11
JournalJournal of Applied Probability
Volume43
Issue number4
DOIs
Publication statusPublished - 2006 Dec 1

Fingerprint

Probability function
Person
Game
Dependent
Nash Equilibrium
Counterexample
Directly proportional
Formulation
Sufficient Conditions
Strategy

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

Cite this

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Two-person red-and-black games with bet-dependent win probability functions. / Chen, May Ru; Hsiau, Shoou Ren.

In: Journal of Applied Probability, Vol. 43, No. 4, 01.12.2006, p. 905-915.

Research output: Contribution to journalArticle

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