A Three-State Markov Model of Choice Behavior within Spatial Structures

摘要

This paper derives a simple mathematical model of spatial learning and choice by integrating several psychological theories, whose features accord with the results of empirical investigation in a previous paper [2]. A sample of homogeneous decision-makers are assumed to make a succession of selections from a given set of initially unknown spatial alternatives (for example, a set of shopping places for a good). The decision-makers pass through two states of “recognition” and “discrimination” learning, before reaching an equilibrium state. In the equilibrium state, decision-makers have sufficiently learned the attributes of the alternatives so that satisfactory choices are always made. These assumptions permit the derivation of mathematical expressions to answer two questions: first, what proportion of decision-makers will be in the equilibrium state after any given time interval, and second, what proportion of decision-makers will choose any designated spatial alternative after the same time interval. In the second case, the proportion of decision-makers choosing an alternative is predicted from the individuals' perceptions of the attributes of the alternatives. The paper concludes with an evaluation of the model and suggestions for its testing and further development.