Report

Teaser, summary, work performed and final results

Periodic Reporting for period 1 - DYNMECH (Dynamic Mechanisms)

Teaser

The project continues be centered around the research questions posed in the grant application. Various research papers are being developed that address different topics. Outlined below are the main papers and how they can contribute to broader objectives. Progress on the...

Summary

The project continues be centered around the research questions posed in the grant application. Various research papers are being developed that address different topics. Outlined below are the main papers and how they can contribute to broader objectives. Progress on the papers is given in the response to subsequent questions.

`Competitive Screening under Heterogeneous Information’ with Renato Gomes and Lucas Maestri. This is the continuation of a paper in progress at the time of the grant application. The problem being addressed is to understand competition in contracts in a theoretical framework. Understanding competition has important social purposes, such as informing antitrust policy.
`Ready to trade? On budget-balanced efficient trade with uncertain arrival’. This paper seeks to understand the constraints on efficiency in institutions operating in dynamic environments. The bilateral trade application relates to an old question in economics regarding the feasibility of efficient trade in settings with asymmetric information. This question is seen as of first-order importance in understanding institutions and markets.
`Robust Predictions of Dynamic Optimal Contracts’ with Alessandro Pavan and Juuso Toikka. We study dynamic mechanisms when agents’ types evolve according to a rich class of stochastic processes. Dynamic mechanism design problems have a broad application across economics, including selling goods, optimal compensation practices and optimal taxation (“dynamic public finance”). The work is intended to feed into these areas
`A dynamic theory of random price discounts,’ with Francesc Dilme. We developed a theory of optimal dynamic pricing where the random evolution of prices ensures consumers are always uncertain about the timing of future discounts. Broadly, this feeds into the theme of uncertainty in dynamic mechanism design; here it is the mechanism, rather than the evolution of agent types, that is uncertain. The paper helps connect both static and dynamic mechanism design literatures to a practical application, which is the apparently randomly timed discounting of goods at many retailers. Again, this feeds into questions in industrial organization, and we argue that the paper could be potentially of interest for antitrust policy.

`Residual Deterrence’ with Francesc Dilme. We developed a theory of dynamic monitoring with costly inspections. We uncover dynamic patterns that could explain real-world phenomena such as “residual deterrence” and “deterrence decay” observed in policing and regulatory settings. Broadly, the work addresses questions about equilibrium monitoring, that will be of interest in dynamic contracting settings, thus relating to the themes and questions of the grant proposal. We believe again that our theory can be used to understand empirical patterns, which attests to its possible social value.

`Fake Sales: A Dynamic Pricing Perspective’. I developed a theory of false claims about price discounting from claimed “regular” price. This short paper uses the ideas of dynamic mechanism design explained in the grant to understand a well-documented phenomenon that is of concern in practice for competition authorities and consumer protection groups.

Work performed

`Competitive Screening under Heterogeneous Information’: This project was underway at the time of the grant proposal and is of integral importance to the grant as providing a foundation for understanding competition in contracts in static environments; while the ongoing work is to look at competition in dynamic environments. We have spent substantial time on this project responding to comments from referees and peers. Importantly, results extending the theory to multiple (rather than two) types were derived and formalized. The paper is now accepted subject to minor revisions at Review of Economic Studies.

`Ready to trade? On budget-balanced efficient trade with uncertain arrival’. A draft manuscript has been completed providing major results in the setting of interest. A key contribution of the paper is to extend the well-known impossibility result for efficient trade in the static setting to a dynamic setting where agents arrive over time.

`Robust Predictions of Dynamic Optimal Contracts’. This paper has been further developed, especially by focusing on results about predictions about the long-run efficiency of optimal dynamic mechanisms in environments where types evolve stochastically according to a broad class of Markov processes. We now have a self-contained draft that includes all our major results.

`A dynamic theory of random price discounts’. We proved a number of results that extend existing knowledge regarding mechanism design with risk averse agents (especially in static auction settings) to dynamic pricing problems. We completed and submitted a version of the paper.

`Residual Deterrence’. This project was underway at the time of the grant. We have continued to develop and present this work, respond to feedback from various audiences and referees. The paper is now accepted at the Journal of the European Economic Association.

`Fake Sales: A Dynamic Pricing Perspective’. The short paper has been started and submitted to a special issue. The main contribution here is an idea: a novel framework for thinking about the question of “fake sales”; a misleading retail practice of concern to consumer rights groups and antitrust authorities.

Final results

Here I highlight some of the main accomplishments of the work that are of particular novelty to the literature in economic theory.
In the `Competitive Screening’ paper we found a way to provide a formal analytic characterization of equilibrium contracts with multiple agent types that has eluded authors of related work (especially Rochet and Stole, 2002). This development allows one to apply our theory in richer settings, and paves the way for richer predictions and also direct empirical application of our model. As mentioned, it also paves the way for considering dynamics.

In `Robust Predictions of Dynamic Optimal Contracts’, we find bounds on the distortions in optimal dynamic contracts and show how these bounds change as the relationship evolves. The approach to bounding surplus losses in a dynamic setting is, to our knowledge, totally new in the literature.

A considerable part of the progress that should be described as beyond the state of the art relates to formulating new ideas; not only methodological developments. For instance, in `A dynamic theory of random price discounts’, the idea that random price discounts observed in practice are part of an optimal dynamic mechanism for the seller is to our knowledge completely new. In `Fake Sales: A Dynamic Pricing Perspective’, the idea to formalize fake sales as a false claim by the seller about future prices is also to my knowledge totally new.