Discrete Choice Models with Different Levels of Utility Uncertainty

Abstract

In this paper, we relax the restriction on the identical distribution for the random utility parts under discrete choice models. The derived new choice model can allow more flexible substitution pattern, and has the potential to describe choice behavior more accurately. If an alternative's nominal utility is relatively high, its choice probability is higher when an individual uses its mean of utility in her choice process, whereas the choice probabilities for other alternatives are lower. We show that in the pricing problem the optimal prices are product-invariant for products with the same levels of utility uncertainty and use this result to simplify the multi-product pricing problem. We also characterize the oligopolistic problems for competition in price and choice probability respectively, and provide efficient algorithms to compute the Nash equilibrium. The assortment problem is generally NP-hard, so we develop a fully polynomial-time approximation scheme that can find an arbitrarily near-optimal solution in a timely manner. Surprisingly, if the utility of a product of the focal firm rather than the outside option is deterministic, the revenue-ordered assortment is optimal for the assortment problem. To implement the newly proposed choice model with different levels of utility uncertainty, we develop an efficient estimation algorithm with estimated product attractiveness in closed form. Several extensions are also considered, including relaxing the restriction under the multi-stage nested logit model.