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Dynamic Mechanisms

Periodic Reporting for period 4 - DYNMECH (Dynamic Mechanisms)

Reporting period: 2021-08-01 to 2023-06-30

The project aims at contributing to the theoretical understanding of dynamic mechanism design and dynamic contracting. Contract theory studies how agreements are reached to determine, for instance, the allocations of goods, payments, and incentives for effort. Much of the literature studies static models. However, many real-world interactions are dynamic in the sense that they take place over time or involve repeated interactions. Dynamics introduces an additional dimension that opens a rich array of questions. Dynamics also introduce an additional layer of complexity that can make the models less analytically tractable, presenting a challenge to the researcher.

The study of dynamic contracting can underpin a deeper understanding of agreements in a broad range of contexts. It potentially feeds through directly to policy. Examples might include lessons about how to better structure government procurement and natural monopoly regulation. Understanding of firm behaviour and pricing decisions could flow through to better informed competition policy. Some of the work could also potentially be picked up by empirical researchers (e.g. so-called "structural" work that brings theoretical models directly to data).

Four principal areas have been considered. (1) Tractable models of dynamic competition in contracts were studied where agents search over time. In these works, as elsewhere in the literature, dispersion of prices or other contractual variables are the result of search frictions and competition. A dynamic model has also been developed that suggests empirically relevant patterns of price dispersion (“sales”) can arise even when competition is absent. (2) Approaches have been developed to study dynamic contracts when an agent or agents' private information evolves randomly over time. One central approach has emphasized that a complete characterisation of the agreement may not be needed to obtain at least some relevant insights about dynamics (e.g. long-run efficiency of the optimal agreements). (3) A result was established showing the difficulty of obtaining efficient bilateral trade when traders' information evolves randomly and when traders arrive to the market over time. (4) Different dynamic models of contracting have been studied where agents make investments, with scope to apply the findings to a range of contexts.
I have (together with co-authors) brought nine papers to publication and completed four working papers. Two of the publications are at “top 5 general interest” journals, and one of the working papers has a second-round revision at such a journal.

Other dissemination. I have presented the work at invited seminars and conferences, making over fifty presentations in total. I have taught my work (in core PhD lectures at Toulouse School of Economics). I undertook a sabbatical at MIT (in the US) where key findings were discussed with faculty. A workshop was held at the University of Essex. I have presented findings to practitioners at a key industry regulator.

Papers include:

(1) Competition in contracts. Work with Renato Gomes and Lucas Maestri (`Competitive Screening under Heterogeneous Information’, `Oligopoly Under Incomplete Information: On the Welfare Effects of Price Discrimination’). Studies the introduction of screening into the dynamic search model of Burdett and Mortensen (1998) (as well as other search models).
`Dynamic Price Competition with Commitment and Search’. Studies pricing commitments by competitors in an environment where buyers learn about the sellers’ offers over time through search.
`A Dynamic Theory of Random Price Discounts’ with Francesc Dilme. Shows in a dynamic setting with arrival of buyers that random price discounts can arise under monopoly, providing an alternative to theories based on competition and search (e.g. Varian, 1980).

(2) Robust predictions in dynamic mechanism design. `Robust Predictions in Dynamic Screening’ with Alessandro Pavan and Juuso Toikka. Shows how to make predictions about the long-run behaviour of optimal dynamic mechanisms when agent information evolves randomly.
`Payoff Implications of Incentive Contracting.’ Shows how to make robust predictions on welfare in static contracting problems, anticipating application to dynamic mechanism design.

(3) Bilateral trade with dynamic arrivals. `Ready to Trade? On Budget-balanced Efficient Trade with Uncertain Arrival.’ Extends Myerson and Satterthwaite’s (1983) impossibility result to dynamic settings with evolving trader information and dynamic arrivals.

(4) Investments in dynamic contracting. For instance, `Relational Contracts: Public versus Private Savings’ with Francesc Dilme. Studies relational or informal agreements when there is dynamic investment in a player’s outside option (through savings).
Key contributions to the economic theory literature include:

`Competitive Screening under Heterogeneous Information’: Finding a way to provide formal analytic characterizations of equilibrium contracts with multiple agent types. Also, providing novel results on welfare implications in the follow-up paper.

`Dynamic Price Competition with Commitment and Search’: Providing a novel model of competition with pricing commitments that provides a way to capture dynamic competition when buyers search over time. Showing an equivalence between equilibrium with commitment to future prices and one where sellers cannot commit but do offer “best price policies” (guarantees to refund customers who find lower prices later). The equivalence has been noted earlier for monopoly, but never for competition.

`A Dynamic Theory of Random Price Discounts’: Showing how buyer risk aversion can yield a theory of random price discounts. In the process, providing novel results on auction-type problems with risk-averse buyers where only the winner pays.

`Robust Predictions in Dynamic Screening’: Demonstrating how one can find bounds on the distortions in optimal dynamic contracts and showing how these bounds change as the relationship evolves.

`Payoff Implications of Incentive Contracts’: Providing for the first time “robust predictions” on welfare in an agency setting with incentives and moral hazard. The approach can naturally be applied to a class of dynamic mechanism design problems (the subject of ongoing work).

`Relational Contracts: Public versus Private Savings’: Characterizing relational contracts with private investments of players in the outside option (which had essentially eluded the literature to date). The approach of partially characterizing the optimal relational contract follows a “perturbation” analysis, conceptually like that in the paper `Robust Predictions of Dynamic Optimal Contracts’.