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.
"Trading cookies in a gambler's ruin scenario." Involve 6 (2) 191 - 220, 2013. https://doi.org/10.2140/involve.2013.6.191