Working Papers:

Batched Adaptive Network Formation

Latest draft (Yan Xu and Bo Zhou, Under review)

Abstract:

Networks are central to many economic and organizational applications, such as workplace team formation, social platform recommendations, and classroom friendship development. In these settings, networks are modeled as graphs, with agents as nodes, agent pairs as edges, and edge weights capturing pairwise production or interaction outcomes. This paper develops an adaptive, or online, policy that learns to form increasingly effective networks over time, progressively improving total network output as measured by the sum of edge weights.

Our approach builds on the weighted stochastic block model (WSBM), which captures agents' unobservable heterogeneity through discrete latent types and models their complementarities in a flexible, nonparametric manner. We frame the online network formation problem as a non-standard batched multi-armed bandit, where each type pair corresponds to an arm, and pairwise reward depends on type complementarity. This strikes a balance between exploration---learning latent types and complementarities---and exploitation---forming high-weighted networks. We establish two key results: a batched local asymptotic normality result for the WSBM and an asymptotic equivalence between maximum likelihood and variational estimates of the intractable likelihood. Together, they provide a theoretical foundation for treating variational estimates as normal signals, enabling principled Bayesian updating across batches. The resulting posteriors are then incorporated into a tailored maximum-weight matching problem to determine the policy for the next batch. Simulations show that our algorithm substantially improves outcomes within a few batches, yields increasingly accurate parameter estimates, and remains effective even in nonstationary settings with evolving agent pools.

Keywords: adaptive network formation, algorithm design, weighted stochastic block model, batched multi-armed bandits, batched local asymptotic normality.

Quantity versus Variety: Non-cooperative Production on an Online Knowledge-Sharing Platform

Latest draft (Maiju Guo, Jian Ni, Qiaowei Shen, and Yan Xu, Under review)

Abstract:

Online question-and-answer platforms allow users to learn and share different perspectives of information and knowledge. Such platforms' performance critically depends on the quantity and variety of knowledge content. This paper studies how the amount of information and the perceived quality of the early knowledge content produced in response to a certainty question influence the growth of knowledge content on the Q&A platform. We study knowledge content growth along the two critical dimensions—quantity and variety. We develop measures of knowledge variety using an unsupervised learning method. Building on a novel data set from the largest Q&A platform, our empirical analysis suggests that early knowledge content substantially influence both the quantity and the variety of future knowledge content production. Specifically, we find that the amount of information in the early knowledge content reduce the quantity of future knowledge production but improve the variety. We also find that a high perceived-quality early knowledge content drives more future knowledge quantity but has no influence on variety. Moreover, we find that the identity (e.g., expert vs. non-expert) of the user moderates the interrelationship between early-stage knowledge contents and future knowledge contents under the same question. Our results provide important managerial insights on how platforms can manage knowledge content production.

Keywords: Q&A platform, quantity-diversity trade-off, unsupervised learning, Doc2Vec

The Relationship between Customer Value and the Timing of Adoption in a New Experience Goods Category

Draft upon request (Yan Xu, Bart Bronnenberg, and Tobias Klein)

Abstract:

We study consumer learning in a new consumer packaged goods category using purchasing data from a long balanced panel. The data are well-suited for this purpose because we observe consumers making their first purchases in the category. We look at the empirical patterns through the lens of a learning model in which consumers make purchase decisions under uncertainty about the values they attach to several brands of an experience good. Their initial prior beliefs regarding the consumption utility they will experience when purchasing products in the category, together with their sensitivity to marketing variables, determine their inclination to adopt. These beliefs are updated after each purchase. In our model, consumers differ not only with respect to their prior beliefs, but also with respect to the value they attach to the products after learning has taken place, as well as their price sensitivity. We allow all these to be related to when they first buy a product from the category. The value consumers attach to the brands, together with their sensitivity to marketing variables, ultimately determines customer value. From a firm's perspective, it is important that marketing variables – promotions and product line length – affect individual utility and, thereby, the inclination to buy a product, and thus also the speed at which consumers learn about their preference for the product. Estimating this structural learning model allows us to characterize learning effects and perform counterfactual simulations. In our counterfactual simulations, we investigate the long-run effect of temporary price promotion, and provide suggestions on optimal temporary price promotion timing decisions.