Attention, Consideration then Selection Choice Model

Manzini and Mariotti [Manzini, Paola, Marco Mariotti. 2014. Stochastic choice and consideration sets. Econometrica 82(3) 1153-1176.] propose a consideration set based choice model that postulates a full preference ordering as well as exogenous attention probabilities from which consideration sets are formed. The model assumes that consumers select the highest ranked product in their consideration set and the heterogeneity among choices are due to randomness in the consideration sets formation process. While Manzini and Mariotti focus on rationalizing this choice model, we look at its operations applicability. We show how to recover the full ordering and attention probabilities given accurate estimates of choice probabilities or from empirical data. Empirical testing of the Random Consideration Set model on our airline partner's data shows that it outperforms the Multinomial Logit choice model in test data over all markets. The Random Consideration Set model also performs better than the Mixture of MNLs model giving a better fit on 67.0% of the markets. We show that an assortment that maximizes expected revenues can be found in $O(n)$ time where $n$ is the number of products. Adding a cardinality constraint increases the complexity to $O(n^2)$. We show that the efficient sets discovery problem can be solved in $O(n^2)$ where the goal is to find an assortment to maximize revenues net of the marginal value of capacity. We extend the Manzini and Mariotti Random Consideration Set model to allow multiple market segments with heterogenous attention probabilities and propose a computationally efficient heuristic with good empirical performance. We also extend the model to allow ties in preferences and show that a revenue-ordered assortment has a 1/2 performance guarantee relative to the optimal assortment. We study the pricing problem where the preference ordering are price aware and show under mild assumptions that optimal profits are such that both the profit contributions and the net value to consumers are aligned with the value gap defined as the difference between the value of the product to consumers and its unit wholesale cost