What is the Impact of Non-Randomness on Random Choice Models?

Abstract

Problem definition. This paper examines the impact of non-randomness on random choice models, and then studies various operations problems under the new discrete choice models. Academic/Practical Relevance. The literature often assumes that the random utility components follow some i.i.d. distribution. This assumption may be too restrictive in some real-world scenarios, because for example some consumers may know well about attribute values for some product (which could also be the no-purchase option) that they have repeatedly purchased. Methodology. We adopt the random utility maximization framework, and characterize the choice probabilities when the utility of some alternative is deterministic. The log-likelihood function is still jointly concave; the EM algorithm is developed to overcome the missing data issue. Results. Surprisingly, if the utility of a particular product is deterministic, the assortment problem is polynomial-time solvable; whereas if the utility of the no-purchase option is deterministic, the assortment problem is NP-hard. We show that the prices are product-invariant at optimality and use this result to simplify the multi-product pricing problems. Managerial Implications. Empirical study on real data shows that incorporating non-randomness into random choice models can increase model fitting and prediction accuracy. Failure of accounting for the impact of non-randomness on random choice models may result in substantial losses.