Learning From Social Interactions: Personalized Pricing and Buyer Manipulation

Abstract

As the sociological theory of homophily suggests, people tend to interact with those of similar preferences. Motivated by this well-established phenomenon, today's online sellers, such as Amazon,~seek~to learn a new buyer's private preference from his friends' purchase records. Although such learning allows the seller to enable personalized pricing and boost revenue, buyers are also increasingly aware of these practices and may alter their social behaviors accordingly. This paper presents the first study regarding how buyers strategically manipulate their social interaction signals considering their preference correlations, and how a seller can take buyers' strategic social behaviors into consideration when designing the pricing scheme. Starting with the fundamental two-buyer network, we propose and analyze a parsimonious model that uniquely captures the double-layered information asymmetry between the seller and buyers, integrating both individual buyer information and inter-buyer correlation information. Our analysis reveals that only high-preference buyers tend to manipulate their social interactions to evade the seller's personalized pricing, but surprisingly, their payoffs may actually worsen as a result. Moreover, we demonstrate that the seller can considerably benefit from the learning practice, regardless of whether the buyers are aware of this fact or not. Indeed, our analysis reveals that buyers' learning-aware strategic manipulation has only a slight impact on the seller's revenue. In light of the tightening regulatory policies concerning data access, it is advisable for sellers to maintain transparency with buyers regarding their access to buyers' social interaction data for learning purposes. This finding aligns well with current informed-consent industry practices for data sharing.

Figures (11)

• Figure 1: Timeline of the dynamic Bayesian game: In Stage I, two buyers $i$ and $j$ socially interact to discuss a new product in the online social network. In Stage II, these buyers sequentially arrive and decide whether to purchase the product or not. The product seller learns the social interaction data from Stage I and then sequentially prices to each arriving buyer in the two consecutive selling periods of Stage II.
• Figure 2: PBE in four regions to tell whether high-preference buyers manipulate their social interaction data with the other high-preference buyer, and how the seller prices in the PBE.
• Figure 3: Comparison of an average buyer's average payoff, when aware versus unaware of the seller's learning (i.e., in the strategic-learning model versus the undisclosed-learning benchmark). As noticed in Table \ref{['table_same']}, the parameter $l$ represents the loss one buyer incurs due to the other buyer's low social response when both buyers have the same high preference.
• Figure 4: Illustration of a network instance with three connected buyers. Here, the upper node represents the known buyer $k$, and the two lower nodes correspond to unknown buyers $i$ and $j$. The two opposing directional arrows connecting any buyer pair indicate their bilateral interactions. Notice that the arrows in this graph do not depict the specific frequency choices of buyers' social interactions.
• Figure 5: Illustration of the three buyers' social interactions in the unique PBE given the upper buyer $k$'s preference is low.

Theorems & Definitions (40)

• Lemma 1
• Lemma 2
• Corollary 1
• Lemma 3
• Definition 1: Manipulation strategy for a high-preference buyer
• Lemma 4
• Proposition 1
• Proposition 2
• Proposition 3
• Proposition 4