Vol. 6, No. 2, 2013

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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
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.

Keywords
excited random walk, cookie environment, gambler's ruin, two-person probabilistic games
Mathematical Subject Classification 2010
Primary: 60J10, 91A05
Milestones
Received: 20 December 2011
Accepted: 14 August 2012
Published: 1 September 2013

Communicated by Anant Godbole
Authors
Kuejai Jungjaturapit
Department of Mathematics
Iowa State University
Ames, IA 50011
United States
Timothy Pluta
Department of Mathematics
North Carolina State University
Raleigh, NC 27695-8205
United States
Reza Rastegar
Department of Mathematics
Iowa State University
Ames, IA 50011
United States
Alexander Roitershtein
Department of Mathematics
Iowa State University
Ames, IA 50011
United States
Matthew Temba
Department of Mathematics
University of Maryland
College Park, MD 20742-4015
United States
Chad N. Vidden
Department of Mathematics
Iowa State University
Ames, IA 50011
United States
Brian Wu
Department of Mathematics
Bowdoin College
Brunswick, ME 04011
United States