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Trading cookies
in a gambler's ruin scenario
Kuejai Jungjaturapit, Timothy Pluta, Reza Rastegar, Alexander Roitershtein, Matthew Temba, Chad N. Vidden and Brian Wu
Vol. 6 (2013), No. 2, 191–220
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Abstract |
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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. |
Keywords
excited random walk, cookie environment, gambler's ruin,
two-person probabilistic games
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Mathematical Subject Classification 2010
Primary: 60J10, 91A05
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Milestones
Received: 20 December 2011
Accepted: 14 August 2012
Published: 1 September 2013
Communicated by Anant Godbole
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Authors |
| Kuejai Jungjaturapit | |
| Department of Mathematics Iowa State University Ames, IA 50011 United States |
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| Timothy Pluta | |
| Department of Mathematics North Carolina State University Raleigh, NC 27695-8205 United States |
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| Reza Rastegar | |
| Department of Mathematics Iowa State University Ames, IA 50011 United States |
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| Alexander Roitershtein | |
| Department of Mathematics Iowa State University Ames, IA 50011 United States |
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| Matthew Temba | |
| Department of Mathematics University of Maryland College Park, MD 20742-4015 United States |
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| Chad N. Vidden | |
| Department of Mathematics Iowa State University Ames, IA 50011 United States |
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| Brian Wu | |
| Department of Mathematics Bowdoin College Brunswick, ME 04011 United States |
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