The Operational Advantages of Threshold Discounting Offers

Abstract

We study threshold discounting, or the practice of offering a discounted-price service if at least a prespecified number of customers signal interest in it, as pioneered by Groupon. We model a capacity-constrained firm, a random-sized population of strategic customers, a desirable hot period, and a less desirable slow period. Compared to a more traditional approach (slow period discounting or closure), threshold discounting has two operational advantages. First, the contingent discount temporally balances demand when the market for the service is large, and reduces supply of the service (preserving higher margins) when the market is small, allowing the firm to respond to the service’s unobserved market potential. Second, activation of the threshold discount signals the market state and the consequent service availability to strategic customers, inducing them into self-selecting the consumption period to one that improves the firm’s capacity utilization. Yet, threshold discounting can be harmful in situations with chronically low demand. In contrast with past work on strategic customers, their presence is advantageous to firms in our context. A calibrated numerical study shows that threshold discounting improves firm profits over a traditional approach by as much as 33% (7% on average). The online appendix is available at https://doi.org/10.1287/mnsc.2017.2740 . This paper was accepted by Yossi Aviv, operations management.

Sales-Based Rebate Design

“…Treating the entire market as a single player with unknown type, where the type determines the operative demand regime, their results can be closely related to the seminal work of Maskin and Riley (1984) which studies optimal quantity discounting of a seller in face of a buyer with uncertain type. 3 Somewhat closer to our work is that of Marinesi et al (2018), where demand uncertainty is present at both ends. A seller with capacity constraints uses threshold discounting to both signal the market size to buyers and to condition offering the product during the "slow" season on the market size, hence reducing the supply-demand mismatch.…”

Contingent stimulus in crowdfunding

“…two types of threshold-induced effects. Marinesi et al (2018) study the benefit of group buying as a means of moderating demand between peaks and troughs. Ming and Tunca (2022) characterize the dynamic sign-up process in group buying by capturing consumer purchase equilibrium with rational expectations of future.…”

Revenue-Maximizing Mechanisms with Strategic Customers and Unknown, Markovian Demand

“…Gallego, Kou and Phillips [2008] (option on callable seats with possible reallocation), Elmaghraby et. al [2009] (selling with future reservations), Jerath, Nettessine, Verarghavan [2009] (opaque sales through an intermediary, so that consumers do not know which brand they get), Osdachyi and Vulcano [2010] (combination of temporal price discrimination with rationing at the low price), Su [2007] (exploitation of differences in patience among customers' patience), Marinesi, Girotra, Netessine [2016] (threshold discounts for group purchasing) Chen and Farias [2015] (limits on the magnitude of price drops) and Borgs et al [2014] (varying capacity in a finite horizon model with deterministic demand). It is fair to say that none of these papers attempts a full mechanism design analysis where optimality is analytically established with respect to a large class of pricing procedures.…”

“…Strategic customers are found to have a beneficial effect in the group buying model of Marinesi, Girotra, Netessine[2016].…”