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2013 Trading cookies in a gambler's ruin scenario
Kuejai Jungjaturapit, Timothy Pluta, Reza Rastegar, Alexander Roitershtein, Matthew Temba, Chad Vidden, Brian Wu
Involve 6(2): 191-220 (2013). DOI: 10.2140/involve.2013.6.191

Abstract

We consider several variations of a two-person game between a “buyer” and a “seller”, whose major component is a random walk of the buyer on an interval of integers. We assume a gambler’s ruin scenario, where in contrast to the classical version the walker (buyer) has the option of consuming “cookies”, which, when used, increase the probability of moving in the desired direction for the next step. The cookies are supplied to the buyer by the second player (seller). We determine the equilibrium price policy for the seller and the equilibrium “cookie store” location. An initial motivation for this question is provided by the popular model of “cookie” or “excited” random walks.

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Kuejai Jungjaturapit. Timothy Pluta. Reza Rastegar. Alexander Roitershtein. Matthew Temba. Chad Vidden. Brian Wu. "Trading cookies in a gambler's ruin scenario." Involve 6 (2) 191 - 220, 2013. https://doi.org/10.2140/involve.2013.6.191

Information

Received: 20 December 2011; Accepted: 14 August 2012; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 1273.91092
MathSciNet: MR3096368
Digital Object Identifier: 10.2140/involve.2013.6.191

Subjects:
Primary: 60J10, 91A05

Rights: Copyright © 2013 Mathematical Sciences Publishers

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