Menu-Dependent Stochastic Feasibility

Abstract

We examine the role of stochastic feasibility in consumer choice using a random conditional choice set rule (RCCSR) and uniquely characterize the model from conditions on stochastic choice data. Feasibility is modeled to permit correlation in availability of alternatives. This provides a natural way to examine substitutability/complementarity. We show that an RCCSR generalizes the random consideration set rule of [Manzini and Mariotti, 2014]. We then relate this model to existing literature. In particular, an RCCSR is not a random utility model.

Stochastic Complementarity

“…The first is the basic Luce (or multinomial logit) model of stochastic choice. The second is (a particular version of) the more recent 'stochastic consideration set' model of Manzini and Mariotti [20] and Brady and Rehbeck [10]. We discover that in both cases the correlation criterion on data reflects novel supermodularity types of condition on preferences.…”

“…However, the recent wave of abstract works on stochastic choice (e.g. Aguiar, Boccardi and Dean [1], Brady and Rehbeck [10], Caplin and Dean [12], Echenique, Saito and Tserenjigmid [16], Gül, Natenzon and Pesendorfer [18], Manzini and Mariotti [20] among others) has highlighted a wide variety of possible 'choice errors' and choice procedures, and so a number of reasons why agents' behaviour might fail to be described by a logit model, and indeed even by the much larger class of RUMs. We take Behavioural Insights Unit established in 2012 as part of the New South Wales Premier and Cabinet's office.…”

Random categorization and bounded rationality

“…In fact, the RC model nests the random consideration set of MM. Also, this model is related to the recent work of Brady and Rehbeck (2014); however the RC is not nested in their contribution. The RC model is nested in the Random Utility representation because it implies Total Monotonicity.…”

“…The random categorization rule is distinct from other efforts to generalize MM and, in particular, it is neither nested nor does it nest the random feasibility rule proposed by Brady & Rehbeck (2015). Recently, Zhang (2016) proposes an empirically different categorization procedure that ours, that produces stochastic choice (e.g., the categories in his work are a partition while here they are arbitrary, among other differences).…”

“…Interestingly, another model that nests MM, provided by Brady and Rehbeck (2014), the Menu Dependent Stochastic Consideration -MDSC-, (also renamed as Random Feasibility) (Brady & Rehbeck, 2014, 2015 is not nested in RC nor is RC nested in their model. Evidently, the intersection of their contribution and the RC rule is non-empty.…”