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Data and Market Design

Paper Session

Sunday, Jan. 8, 2023 8:00 AM - 10:00 AM (CST)

Hilton Riverside, Chequers
Hosted By: Econometric Society
  • Chair: Marzena Joanna Rostek, University of Wisconsin-Madison

Is Selling Complete Information (Approximately) Optimal?

Dirk Bergemann
,
Yale University

Abstract

We study the problem of selling information to a data-buyer who faces a decision problem under uncertainty. We consider the classic Bayesian decision-theoretic model pioneered by Blackwell [Bla51, Bla53]. Initially, the data buyer has only partial information about the payoff-relevant state of the world. A data seller offers additional information about the state of the world. The information is revealed through signaling schemes, also referred to as experiments. In the single-agent setting, any mechanism can be represented as a menu of experiments. A recent paper by Bergemann et al. [BBS18] present a complete characterization of the revenue-optimal mechanism in a binary state and binary action environment. By contrast, no characterization is known for the case with more actions. In this paper, we consider more general environments and study arguably the simplest mechanism, which only sells the fully informative experiment. In the environment with binary state and m ≥ 3 actions, we provide an O(m)-approximation to the optimal revenue by selling only the fully informative experiment and show that the approximation ratio is tight up to an absolute constant factor. An important corollary of our lower bound is that the size of the optimal menu must grow at least linearly in the number of available actions, so no universal upper bound exists for the size of the optimal menu in the general single-dimensional setting. We also provide a sufficient condition under which selling only the fully informative experiment achieves the optimal revenue. For multi-dimensional environments, we prove that even in arguably the simplest matching utility environment with 3 states and 3 actions, the ratio between the optimal revenue and the revenue by selling only the fully informative experiment can grow immediately to a polynomial of the number of agent types. Nonetheless, if the distribution is uniform, we show that selling only the fully informative experiment is indeed the optimal mechanism.

Artificial Intelligence and Auction Design

Martino Banchio
,
Stanford University
Andy Skrzypacz
,
Stanford University

Abstract

Motivated by online advertising auctions, we study auction design in repeated auctions played by simple Artificial Intelligence algorithms (Q-learning). We find that first-price auctions with no additional feedback lead to tacit-collusive outcomes (bids lower than values), while second-price auctions do not. We show that the difference is driven by the incentive in first-price auctions to outbid opponents by just one bid increment. This facilitates re-coordination on low bids after a phase of experimentation. We also show that providing information about lowest bid to win, as introduced by Google at the time of switch to first-price auctions, increases competitiveness of auctions.

Fair Prediction with Endogenous Behavior

Christopher Jung
,
University of Pennsylvania
Sampath Kannan
,
University of Pennsylvania
Changhwa Lee
,
University of Pennsylvania
Mallesh M. Pai
,
Rice University
Aaron Roth
,
University of Pennsylvania
Rakesh Vohra
,
University of Pennsylvania

Abstract

There is increasing regulatory interest in whether machine learning algorithms deployed in consequential domains (e.g. in criminal justice) treat different demographic groups ``fairly.' However, there are several proposed notions of fairness, typically mutually incompatible. Using criminal justice as an example, we study a model in which society chooses an incarceration rule. Agents of different demographic groups differ in their outside options (e.g. opportunity for legal employment) and decide whether to commit crimes. We show that equalizing type I and type II errors across groups is consistent with the goal of minimizing the overall crime rate; other popular notions of fairness are not.

Robustly Optimal Mechanisms for Selling Multiple Goods

Yeon-Koo Che
,
Columbia University
Weijie Zhong
,
Stanford University

Abstract

We study robustly optimal mechanisms for selling multiple items. The seller maximizes revenue against a worst-case distribution of a buyer’s valuations within a set of distributions, called an “ambiguity” set. We identify the exact forms of robustly optimal selling mechanisms and the worst-case distributions when the ambiguity set satisfies a variety of moment conditions on the values of subsets of goods. We also identify general properties of the ambiguity set that lead to the robust optimality of partial bundling which includes separate sales and pure bundling as special cases.

Discussant(s)
Jacopo Perego
,
Columbia University
Annie Liang
,
Northwestern University
Max Kasy
,
University of Oxford
Modibo Camara
,
Northwestern University
JEL Classifications
  • D47 - Market Design
  • D44 - Auctions