Richard Zeckhauser

Jamie Tucker-Foltz, Richard Zeckhauser

A single seller offers one or more goods to a single buyer. The buyer's values and the seller's costs are private information. Each player has a commonly known prior over the other player's value or cost, supported on a finite set. What is the optimal selling mechanism? We argue that, despite this question's importance and apparent simplicity, prior work offers no satisfactory answer. If the seller simply chooses an optimal menu given her realized costs, she fails to exploit her informational advantage. At the other extreme, the optimal trade mechanism that satisfies IC/IR constraints for both parties fails in practice, as it conditions prices on the seller's unknown costs in an unenforceable way. The seller's realistic capabilities lie somewhere in between: she may leverage private information but lacks unlimited commitment power. To bridge this gap, we consider a solution concept built on the realistic assumption that the seller can commit to prices but nothing more. Similar -- albeit technically distinct -- solution concepts have been studied in the context of auctions with multiple buyers. Our concept proves surprisingly rich even with a single buyer. In our model, the buyer and seller engage in multiple rounds of cheap talk before the seller posts a menu of priced bundles. The buyer then purchases. We measure value as profit for the seller and consumer surplus for the buyer. We prove that with a single good cheap talk cannot help either party, but show that it creates value in any extension of this canonical setting: multiple goods, multiple units, interdependent values, or repeated play. We also show that multiple rounds of communication can yield strictly higher expected profit than a single round. Finally, we discuss how realistic factors beyond our stripped-down model combine with cheap talk to enhance this value even further.

Anmol Kagrecha, Henrik Marklund, Potsawee Manakul et al.

Human feedback is increasingly used across diverse applications like training AI models, developing recommender systems, and measuring public opinion -- with granular feedback often being preferred over binary feedback for its greater informativeness. While it is easy to accurately estimate a population's distribution of feedback given feedback from a large number of individuals, cost constraints typically necessitate using smaller groups. A simple method to approximate the population distribution is regularized averaging: compute the empirical distribution and regularize it toward a prior. Can we do better? As we will discuss, the answer to this question depends on feedback granularity. Suppose one wants to predict a population's distribution of feedback using feedback from a limited number of individuals. We show that, as feedback granularity increases, one can substantially improve upon predictions of regularized averaging by combining individuals' feedback in ways more sophisticated than regularized averaging. Our empirical analysis using questions on social attitudes confirms this pattern. In particular, with binary feedback, sophistication barely reduces the number of individuals required to attain a fixed level of performance. By contrast, with five-point feedback, sophisticated methods match the performance of regularized averaging with about half as many individuals.

Anmol Kagrecha, Henrik Marklund, Benjamin Van Roy et al.

Common crowdsourcing systems average estimates of a latent quantity of interest provided by many crowdworkers to produce a group estimate. We develop a new approach -- predict-each-worker -- that leverages self-supervised learning and a novel aggregation scheme. This approach adapts weights assigned to crowdworkers based on estimates they provided for previous quantities. When skills vary across crowdworkers or their estimates correlate, the weighted sum offers a more accurate group estimate than the average. Existing algorithms such as expectation maximization can, at least in principle, produce similarly accurate group estimates. However, their computational requirements become onerous when complex models, such as neural networks, are required to express relationships among crowdworkers. Predict-each-worker accommodates such complexity as well as many other practical challenges. We analyze the efficacy of predict-each-worker through theoretical and computational studies. Among other things, we establish asymptotic optimality as the number of engagements per crowdworker grows.