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Please use this identifier to cite or link to this item: http://ir.ncue.edu.tw/ir/handle/987654321/16708

Title: Two-Person Red-and-Black Games with Bet-Dependent Win Probability Functions
Authors: Chen, May-Ru;Hsiau, Shoou-Ren
Contributors: 數學系
Keywords: Red-and-black game;Bold strategy;Timid strategy;Convex function;Nash equilibrium
Date: 2006-12
Issue Date: 2013-06-05T07:41:08Z
Publisher: Applied Probability Trust
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.
Relation: Journal of Applied Probability, 43(4): 905-915
Appears in Collections:[數學系] 期刊論文

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