Transient and Asymptotic Behavior of a Random-Utility Based Stochastic Search Process in Continuous Space and Time

Leonardi, G. (1983). Transient and Asymptotic Behavior of a Random-Utility Based Stochastic Search Process in Continuous Space and Time. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-83-108

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Abstract

The paper explores the properties of some simple search and choice behaviors, by exploiting the asymptotic properties of maxima of sequences of random variables. Heterogeneity in the preference is introduced by means of additive random utilities, and the actor is assumed to choose points in a plane region, by sampling them according to a stochastic process. It is shown that asymptotic convergence to a Logit model holds under considerably weaker assumptions than those commonly found in the literature to justify it. This asymptotic property is treated in details for utility-maximizing behavior, and outlined for satisficing behavior. The asymptotic equivalence of the two behaviors suggests that progress in widening the family of asymptotically Logit-equivalence behaviors can be made with further research.

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