Reference-based transitions in short-run price elasticity

Marketing literature has long recognized that price response need not be monotonic and symmetric, but has yet to provide generalizable market-level insights on reference price type, asymmetric thresholds and sign and magnitude of elasticity transitions. In this paper, we introduce smooth transition models to study reference-based price response across 25 fast moving consumer good categories. Our application to 100 brands shows that 77% demonstrate reference-based price response, of which 36% reflects historical reference prices, 31% reflects competitive reference prices, and 33% reflects both types of reference prices. This reference-based price response shows asymmetry for gains versus losses on three levels: the threshold size, the sign and the magnitude of the elasticity difference. For historical reference prices, the threshold size is larger for gains (20%) than for losses (12%) and the assimilation/contrast effects for gains (-0.41) are smaller than the saturation effects for losses (0.81). For competitive reference prices, the threshold size is smaller for gains (3%) than for losses (16%), and the saturation effects are larger for gains (0.33) than for losses (0.15). These results are moderated by both brand and category characteristics that affect reference price accessibility and diagnosticity. Historical reference prices more often play a role for national brands, for planned purchases and in inexpensive categories with low price volatility and high purchase frequency. When price discounting, high-share brands face larger latitudes of acceptance. When raising prices, saturation effects set in later for brands with high price volatility and for categories with high price spread and for planned purchases. As for competitive reference prices, saturation effects set in later for expensive brands with high price volatility and in categories with lower price volatility, higher price spread and higher concentration. Sales, revenue and margin implications are illustrated for price changes typically observed in consumer markets.asymmetric price thresholds;competitive versus historical reference prices;empirical generalizations;kinked demand curve;saturation versus assimilation/contrast effects;smooth-transition regression models

Utility Fairness in Contextual Dynamic Pricing with Demand Learning

This paper introduces a novel contextual bandit algorithm for personalized pricing under utility fairness constraints in scenarios with uncertain demand, achieving an optimal regret upper bound. Our approach, which incorporates dynamic pricing and demand learning, addresses the critical challenge of fairness in pricing strategies. We first delve into the static full-information setting to formulate an optimal pricing policy as a constrained optimization problem. Here, we propose an approximation algorithm for efficiently and approximately computing the ideal policy. We also use mathematical analysis and computational studies to characterize the structures of optimal contextual pricing policies subject to fairness constraints, deriving simplified policies which lays the foundations of more in-depth research and extensions. Further, we extend our study to dynamic pricing problems with demand learning, establishing a non-standard regret lower bound that highlights the complexity added by fairness constraints. Our research offers a comprehensive analysis of the cost of fairness and its impact on the balance between utility and revenue maximization. This work represents a step towards integrating ethical considerations into algorithmic efficiency in data-driven dynamic pricing

Context-Based Dynamic Pricing with Online Clustering

We consider a context-based dynamic pricing problem of online products which have low sales. Sales data from Alibaba, a major global online retailer, illustrate the prevalence of low-sale products. For these products, existing single-product dynamic pricing algorithms do not work well due to insufficient data samples. To address this challenge, we propose pricing policies that concurrently perform clustering over products and set individual pricing decisions on the fly. By clustering data and identifying products that have similar demand patterns, we utilize sales data from products within the same cluster to improve demand estimation and allow for better pricing decisions. We evaluate the algorithms using the regret, and the result shows that when product demand functions come from multiple clusters, our algorithms significantly outperform traditional single-product pricing policies. Numerical experiments using a real dataset from Alibaba demonstrate that the proposed policies, compared with several benchmark policies, increase the revenue. The results show that online clustering is an effective approach to tackling dynamic pricing problems associated with low-sale products. Our algorithms were further implemented in a field study at Alibaba with 40 products for 30 consecutive days, and compared to the products which use business-as-usual pricing policy of Alibaba. The results from the field experiment show that the overall revenue increased by 10.14%