Periodic Reporting for period 3 - DYNMECH (Dynamic Mechanisms) Reporting period: 2020-01-01 to 2021-07-31 Summary of the context and overall objectives of the project The project is being carried out by developing several research papers. The specific objectives are best discussed in relation to each. `Competitive Screening under Heterogeneous Information’ with R Gomes and L Maestri. The problem being addressed is to understand competition in contracts in a theoretical framework`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. `Robust Predictions of Dynamic Optimal Contracts’ with A Pavan and J 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 F 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. `Residual Deterrence’ with F 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. `Fake Sales: A Dynamic Pricing Perspective’. I developed a theory of false claims about price discounting from the claimed “regular” price. `Payoff Implications of Incentive Contracts.’ This paper considers the “robust predictions” that an outside observer to an agency relationship can make when lacking information about the agent’s preferences for exerting effort. `Relational Contracts: Public versus Private Savings’ with F Dilme. This paper explores dynamic contracting with an agent who has consumption smoothing preferences. As usual in relational contracting problems, the principal cannot commit to the contract offered; instead it must be self-enforcing. `Project Design’ with G Georgiadis, A Smolin and B Szentes. This is related also to the paper `Payoff Implications of Incentive Contracts’ above, but the setting is more in the framework of traditional moral hazard.`Oligopoly under Incomplete Information: On the Welfare Effects of Price Discrimination’ with Renato Gomes and Lucas Maestri. This paper uses the competitive search framework in the above mentioned paper to look at the welfare implications of price discrimination. Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far `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. The paper is now published at the Review of Economic Studies.`Ready to trade? On budget-balanced efficient trade with uncertain arrival’. The paper received a “reject and resubmit” at the Journal of Economic Theory and I plan to resubmit the paper.`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.`A dynamic theory of random price discounts’. We proved a number of results that extend existing knowledge regarding mechanism design with risk averse agents to dynamic pricing problems. This paper is currently “revise and resubmit” at the American Economic Review. `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 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. The paper is now forthcoming in a special issue of the Japanese Economic Review The paper `Payoff Implications of Incentive Contracts’ has now been published at Theoretical Economics. This paper was a winner of the Econometric Society European Meetings best paper in applied economics by a young researcher.The paper `Relational Contracts: Public versus Private Savings’ is now “revise and resubmit” at Econometrica.The paper `Project Design’ is currently under review at the American Economic Review. Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far) 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.The work `Payoff Implications of Incentive Contracts’ is the first to consider the “robust predictions” that can be made in an agency setting. It provides an approach to characterizing the set of expected payoffs of the players that is methodologically new. Because the problem is novel, there is no counterpart to these methods in existing literature.The paper `Relational Contracts: Public versus Private Savings’, as mentioned above, is also a very new direction for this literature. Although the setting seems very canonical, it is difficult to determine properties of the optimal contract. The approach depends partly on a “perturbation” analysis, which is conceptually similar to what is done in the paper `Robust Predictions of Dynamic Optimal Contracts’.In addition, 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 my knowledge completely new.The paper `Project Design’ is taking a very novel look at an old question. While a huge literature studies moral hazard problems, this will be the first paper to view the agent as designing the moral hazard problem. Solving the problem necessitates and entirely original approach.