Research

An agent privately observes his project's success and chooses when to submit it to a principal, who observes only a noisy signal; because success is unverifiable, he may submit before it has actually arrived, a behavior I call spoofing. With a single submission, the unique equilibrium is stationary. With resubmission, the standard is constant within each round but varies non-monotonically across rounds, alternating around the unlimited-resubmission standard; the round exactly one chance before any cap binds is the strictest in the entire model. Unlimited resubmission leaves the agent strictly worse off than a single submission at every discount and arrival rate, though the principal gains when sufficiently patient. This divergence is not just distributional: because neither player internalizes the cost their preferred cap imposes on the other, the socially optimal cap lies strictly between the agent's, always one submission, and the principal's, which can be unlimited.

In referral programs, attribution rules determine whether intermediaries are compensated only for focal conversions or also for the downstream platform value of referred consumers. We study this tension in affiliate marketing, where posted cookie duration and related eligibility rules determine an effective cookie duration: the extent to which affiliates are rewarded for spillover value from referred traffic in addition to immediate conversion on the linked product.

Crucially, this affects the strategic interaction among affiliates. Affiliates receive independent signals about many products. They can conform on recommending a salient product, aggregating information and increasing the probability of a quick sale, or disperse across alternatives, preserving opportunities to capture later clicks. We show that, for a fixed effective cookie duration, affiliates' preferred recommendation regime need not be an equilibrium. Affiliates prefer conformity when compensation is sufficiently sale-oriented, but it is an equilibrium only for intermediate effective cookie durations. Non-conformity is always an equilibrium.

The platform's optimal design accounts for both affiliates' preferences and equilibrium feasibility. When immediate conversion is central, the optimal design prescribes an intermediate effective cookie duration that supports conformity. When referred traffic generates sufficient spillover value, it warrants a longer effective cookie duration to support recommendation dispersion and increase expected visits. Consumers prefer conformity because it helps them find a high-quality product with less search, so platform and consumer preferences align when conversion matters most but diverge when traffic spillovers dominate. The implementation thresholds decrease as consumers' expected search lengthens, platform spillover value increases, and affiliate information becomes more precise.

In many advice markets, experts often assertively recommend that clients take a specific action, but they are vague about the probability of the action's outcomes, making the recommendation ambiguous. This paper analytically investigates this phenomenon and the mechanism of the underlying marketing tactic by incorporating the client's optimism and attitudes toward ambiguity into a strategic communication framework. 

In equilibrium, the expert will assert a range of probabilities within which the recommended action turns desirable for the client, whose lower end is strictly below the precise observation based on his or her expertise. When the client cannot exert effort to disambiguate the expert's message, the expert benefits from the client's greater optimism and lower aversion to ambiguous information. Interestingly, when the client exerts costly effort, the expert can leverage the client's ambiguity attitude. As the client becomes more ambiguity averse, precise information about the less preferable option becomes even less preferable, so that the client's greater ambiguity aversion mitigates the ambiguity of the information about the focal option, inducing the expert to send a more ambiguous message.

In influencer marketing, marketers can leverage the attention of followers through sponsored content posted by influencers and social learning among followers via interactions with these posts. We explore how a marketer can optimally leverage influencer marketing using these distinctive features. The decision to encourage social learning or to focus solely on awareness depends on the initial uncertainty of the product quality, and the amount of resulting learning depends on the endogenous influencer's choice of creative contribution to the campaign. 

Social learning is valuable to the marketer only if the option value from learning is high because the brand is relatively unknown a-priori. When influencers value consumer surplus, they create less creative (and more informative) content than what is optimal for the marketer in terms of learning. Furthermore, our analysis demonstrates that for an unknown brand, a mega influencer with a large following fosters more information aggregation and yields higher profits. In contrast, for an established brand, using many micro-influencers with fewer followers yields higher profits by creating attention while minimizing learning about the product. Our model also explains why influencer campaigns either "go viral" or "go bust."

Social media influencers allow marketers to reach audiences using more authentic and credible messaging. Among influencers, marketers need to decide which types of influencers to contract with, what information to give them and how much to pay them.

We analyze the impact of influencer recommendation types on marketer profits, consumer satisfaction, and influencer payoffs. Counter to intuition, we find that shallow influencers, who promote the marketer's message as is, increase market transparency, consumer satisfaction and marketer profits. However, prudent influencers, who carefully review products they promote, entice the marketers to reduce information efficiency in the market, and increase the share of unsatisfied consumers through Bayesian persuasion. In a market with simultaneously active shallow and prudent influencers, prudent influencers may increase their payoff even further by extracting additional information rent.

The results provide insight into the value of shallow influencers and guidance for marketers who consider using influencer marketing.

1. Irreducibility of the Hilbert schemes of points on surfaces with Kleinian singularities. Communications in Algebra, 51(1), 98-115, 2023.

2. Counterexamples of Kodaira vanishing for smooth surfaces of general type in positive characteristic. Journal of Pure and Applied Algebra, 221(10), 2431-2444, 2017.