The Optimality of Choice by Markov Random Walk

In the rational choice problem Zutler (2011) proposed a model of choice by continuous Markov random walk on a set of alternatives to find the best. In this paper we investigate the optimal properties of obtained solutions. It is shown that the result of this choice is the maximal element on a set of lotteries with respect to relation p > q iff F(p, q) > F(q, p) for special function F(., .) that has a natural interpretation as flow of probability from one to another lottery. It is shown the relationship between the problems of choosing the best alternative and non-cooperative games solution. It is proved that Nash equilibrium is a stationary point of a dynamical system of the continuous random walk of players on the set of available strategies. The intensity transition of the player from one strategy to another is equal to his assessment of increase of payoff in the alleged current rival's strategies.