When Prospect Theory Meets Consumer Choice Models: The Role of Reference Prices

The multinomial logit (MNL) model, along with other discrete choice models, has been widely used in economics, marketing, behavioral science, transportation, and other fields by researchers and practitioners for roughly half century since the pioneer work by Robert Duncan Luce and Daniel McFadden; see  Luce (1959) and McFadden (1974). Under the MNL model, each individual chooses the alternative with the highest outcome utility, which is consistent with the random utility maximization. Daniel Kahneman and Amos Tversky created and developed the prospect theory four decades ago as a psychologically more accurate description of decision making than the utility theory; see the seminar paper by Kahneman and Tversky (1979) in behavioral economics. According to the prospect theory, individuals make decisions based on the potential value of losses and gains rather than the final outcome. In our recent paper (Wang 2018), we introduce the reference price to bridge the gap between the prospect theory and the MNL model, the two pieces of Nobel prize-winning work in economics.

Reference prices arise as price expectations against which customers evaluate products in their purchase scenarios. Reference prices are the points against which customers decide their willingness to pay for the products they are considering. Repeated customers may remember the prices encountered on the past purchase occasions, so they may adapt to or assimilate past prices of the product they purchased or considered. However, it is documented that people have consistently demonstrated a limited ability to recall the prices they paid before. Unlike time in the past prices, some customers evaluate the price of a product by comparing with the prices of other products in the same category. The prices of other products may also be taken into account in the evaluation of a particular product during the choice process. The external information on other products in this purchase environment determines what customers think they should pay for a particular product, which impacts their choice behavior. This kind of effect is referred to as an external reference price or simply reference price. Because the formation of a reference price involves a comparison between the price of a product and the current prices of other products, it captures the effects of this reference price across products.

How do customers form their reference prices? Are these reference prices mostly related to the lowest, the highest, the median, the average market prices or the price of a particular product? The lowest price may play an important role in product evaluation, because it is often featured in local newspapers or displayed in the best shelf location. The price of a particular product, for example the store brand, may form another reference price. In addition, assortment variety may also affect the evaluation of certain products. In this paper (Wang 2018), we incorporate reference prices into the MNL model, validate the importance by empirical study and investigate the impact of various reference prices on choice behavior, as well as on assortment planning and pricing.

The MNL model exhibits a restrictive substitution pattern, known as the independence of irrelevant alternatives (IIA) property, a special case of the so-called simple scalability. Simple scalability implies the order of the choice probabilities for any two alternatives—not necessarily the ratio—is independent of the offer set or the attributes of other alternatives. In particular, if one alternative is preferred to another in one scenario, it is preferred in any other scenario. However, the order of the choice probabilities does not necessarily hold if a reference price exists. If the changes of the offer set or prices lead to a dramatically different reference price, the preference order may reverse, because the changes of utility or disutility due to the reference price may overwhelm others.

Under many other choice models including the MNL and preference-based choice models, consumer surplus is always higher as more products are offered or the attractiveness of some existing products is higher by, for instance, increasing feature values or decreasing prices. Different from these choice models, the “more is not always better” phenomenon may happen under the reference-dependent choice models; that is, consumer surplus may be lower due to the effects of different reference prices by offering new products or reducing prices of existing products. The choice models with reference prices allow more flexible substitution patterns.

Our empirical study on a data set about ketchup brands shows that incorporating reference prices into choice models can significantly improve the goodness-of-fit and prediction accuracy of choice behavior. Moreover, the reference prices (e.g., the lowest price and the store brand price) play an important role in brand choices in this ketchup data set. In addition, we also show that failure to account for reference prices may lead to substantial losses in some scenarios, where the reference price effects indeed exist. Therefore, incorporating reference prices into consumer choice models and investigating the associated assortment planning and pricing problems are necessary. If the reference price is defined by the lowest price, we show that a quasi-markup-ordered assortment, which includes products following the markup-decreasing order plus at most one additional item, is optimal. For the pricing problem, we show that the same-markup/same-price policy, which charges the same markup for high-cost products and the same price for low-cost products, is optimal.

Reference price integrates the prospect theory and discrete choice models, and therefore will shed light on a new way to investigate bounded rationality or risk in decision making. Further study on the formation of reference prices and the impact on choice behavior and operations management would be interesting and potentially useful for researchers and practitioners.



Kahneman D, Tversky A (1979) Prospect theory: An analysis of decision under risk. Econometrica 47(3):263–291.

Luce RD (1959) Individual Choice Behavior: A Theoretical Analysis (Wiley, New York).

McFadden D (1974) Conditional logit analysis of qualitative choice behavior. Zarembka P, ed. Frontiers in Econometrics (Academic Press, New York), 105–142.

Wang R (2018) When prospect theory meets consumer choice models: assortment and pricing management with reference prices. Manufacturing Service Operations Management 20(3):583–600.