nicholas wu


Working Papers

Sharing the Credit for Joint Research

draft available upon request

Managed Campaigns and Data-Augmented Auctions for Digital Advertising

with Dirk Bergemann and Alessandro Bonatti, draft available upon request


We develop an auction model for digital advertising that accounts for three defining features of digital markets: (i) advertisers can reach at least a fraction of their customers outside of the digital platforms; (ii) advertising allocations on digital platforms are supported by additional data that improves the match quality between viewers and advertisers, and (iii) matching occurs through auction-like mechanisms. The model considers a monopoly platform that offers an auction mechanism for digital advertising. As an intermediary, the platform has access to additional data about the value of matches between advertiser and consumer. It can therefore support bidding with additional information and increase the feasible surplus for on-platform matches. The advertisers jointly determine their pricing strategy on and off the platform, as well as their bidding for digital advertising on the platform. In a data-augmented second-price auction, the advertisers increase the product prices off the platform to be more competitive on the platform. The resulting allocation is socially efficient and enabled by the data on the platform. This contrasts with the allocation off the platform, which displays inefficiency due to excessively high product prices. We then compare the second price auction with a managed campaign mechanism. Here the advertisers submit budgets that are then transformed into matches and prices through an autobidding algorithm. The managed campaign mechanism can increase the revenue of the digital platform relative to the data-augmented second price auction. With sufficient competition among advertisers, it also increases the surplus of the consumers on and off the platform.
Maximizing the Effect of Altruism

with Nicole Immorlica and Brendan Lucier, draft available upon request


We study the problem faced by an altruistic donor who wants to allocate a fixed set of funds to increase the production of a good. The good is produced by one or more profit-maximizing firms that sell it in an imperfectly competitive downstream market. The firms have private types that determine their (convex and increasing) costs of production, whereas the market outcome and prices are publicly observed. For the case of a single firm, we show that the altruist's optimal mechanism takes the form of a menu of subsidies that offer payments to the firm as a function of its change in production. The optimal solution exhibits pooling of the most efficient types of producer while separating the less efficient types. Offering a single menu item is optimal under sufficiently pessimistic beliefs. We further show that a per-unit subsidy is generically suboptimal. When there are multiple firms, we show that the altruist's impact is decreasing in the size of the competitive externalities that the firms exert on each other.
Explainable Machine Learning Models of Consumer Credit Risk

with Randall Davis, Andrew Lo, Sudhanshu Mishra, Arash Nourian, Manish Singh, and Ruixun Zhang


In this paper, we create machine learning (ML) models to forecast home equity credit risk for individuals using a real-world dataset and demonstrate methods to explain the output of these ML models to make them more accessible to the end-user. We analyze the explainability of these models for various stakeholders: loan companies, regulators, loan applicants, and data scientists, incorporating their different requirements with respect to explanations. For loan companies, we generate explanations for every model prediction of creditworthiness. For regulators, we perform a stress test for extreme scenarios. For loan applicants, we generate diverse counterfactuals to guide them with steps to reverse the model's classification. Finally, for data scientists, we generate simple rules that accurately explain 70-72% of the dataset. Our work is intended to accelerate the adoption of ML techniques in domains that would benefit from explanations of their predictions.