Consumer Choice with Consideration Set: Threshold Luce Model

This paper investigates the threshold Luce model, a recently proposed choice model with a threshold for the consideration-set formation. Under the threshold Luce model, consumers first form their consideration set: If an alternative with significantly low utility is dominated by another one, it will not be included in the consideration set. The threshold Luce model can alleviate the independence of irrelevant alternatives (IIA) property and allow more flexible substitution patterns. We characterize the optimal strategy and develop efficient solutions for price and assortment optimization problems. Under the threshold Luce model, the price competition may have zero, one, two, or infinite Nash equilibria, depending on the magnitude of the threshold effect. Moreover, we also develop an efficient estimation method to calibrate the threshold Luce model. Our numerical study on synthetic and real data sets shows that the new model can improve the goodness of fit and prediction accuracy of consumer choice behavior, which suggests the threshold effect should be taken into account in decision making.