The sequential alternative search as a continuous Markov random walk

The course of the process is analyzed for the choice by an individual of alternatives from a few alternatives, among which he has paired preferences, possibly intransitive and probabilistic. It is supposed that the individual carries out the choice with the aid of the process of the sequential exhaustive search of alternatives, on which a number of conditions (axioms) are imposed. It is shown that in this case the process is modeled by the continuous Markov random walk in the set of alternatives; the intensities of transitions are equal to the comparative utility function; the choice result will be probabilistic and will correspond to the established probability distribution in the random walk. It is shown that the choice result will be the Nash equilibrium in the game, which is set up on the paired preferences of the individual.