nep-cta New Economics Papers
on Contract Theory and Applications
Issue of 2022‒09‒19
seven papers chosen by
Guillem Roig
University of Melbourne

  1. Revelation principle under strategic uncertainty: application to financial contracts with limited liability By Dai ZUSAI
  2. Pricing Novel Goods By Francesco Giovannoni; Toomas Hinnosaar
  3. Timing Moral Hazard under Deductibles in Health Insurance By Zabrodina, V.;
  4. Get It in Writing: Formal Contracts Mitigate Social Dilemmas in Multi-Agent RL By Phillip J. K. Christoffersen; Andreas A. Haupt; Dylan Hadfield-Menell
  5. Myerson on a Network By Rangeet Bhattacharyya; Palash Dey; Swaprava Nath
  6. Dynamic Price Competition: Theory and Evidence from Airline Markets By Ali Hortaçsu; Aniko Oery; Kevin R. Williams
  7. Licensing in a Stackelberg industry, product differentiation, and welfare By Antelo, Manel; Bru, Lluís

  1. By: Dai ZUSAI
    Abstract: We consider a principal-agent model in which the principal can terminate the agent's project and an outsider can affect the project's result. Only the agent can observe the outsider's action and sends a message to the principal. Under strategic uncertainty about the outsider's action in complete information, sequential equilibrium is a suitable equilibrium concept to select the robust outcome and to completely identify the underlying posterior belief. We prove the revelation principle for sequential equilibrium in such a game. Based on this revelation principle, we present a legitimate and simple form of the limited liability constraint on a financial contract that is robust to strategic uncertainty.
    Date: 2022–08
  2. By: Francesco Giovannoni; Toomas Hinnosaar
    Abstract: We study a buyer-seller problem of a novel good for which the seller does not yet know the production cost. A contract can be agreed upon at either the ex-ante stage, before learning the cost, or at the ex-post stage, when both parties will incur a costly delay, but the seller knows the production cost. We show that the optimal ex-ante contract for a profit-maximizing seller is a fixed price contract with an "at-will" clause: the seller can choose to cancel the contract upon discovering her production cost. However, sometimes the seller can do better by offering a guaranteed-delivery price at the ex-ante stage and a second price at the ex-post stage if the buyer rejects the first offer. Such a "limited commitment" mechanism can raise profits, allowing the seller to make the allocation partially dependent on the cost while not requiring it to be embedded in the contract terms. Analogous results hold in a model where the buyer does not know her valuation ex-ante and offers a procurement contract to a seller.
    Date: 2022–08
  3. By: Zabrodina, V.;
    Abstract: This paper develops a new approach to identifying timing moral hazard in health insurance contracts when deductible choice is endogenous. I set up a dynamic model of healthcare consumption where individuals exceed a high deductible after a large health shock. I show that individuals either strategically prepone care from the year after the shock and keep a high deductible, or do not retime and switch to a low deductible the year after. The identification of timing moral hazard exploits the randomness of shock timing within a calendar year. Empirical results show quantitatively significant timing moral hazard responses, which decrease with the time left to the deductible reset. This pattern suggests that there are substantial frictions to preponing, and that dynamic changes in incentives matter in shaping strategic timing responses.
    Keywords: health insurance; strategic timing; moral hazard; insurance plan choice;
    JEL: D82 I11 I13
    Date: 2022–07
  4. By: Phillip J. K. Christoffersen; Andreas A. Haupt; Dylan Hadfield-Menell
    Abstract: Multi-agent reinforcement learning (MARL) is a powerful tool for training automated systems acting independently in a common environment. However, it can lead to sub-optimal behavior when individual incentives and group incentives diverge. Humans are remarkably capable at solving these social dilemmas. It is an open problem in MARL to replicate such cooperative behaviors in selfish agents. In this work, we draw upon the idea of formal contracting from economics to overcome diverging incentives between agents in MARL. We propose an augmentation to a Markov game where agents voluntarily agree to binding state-dependent transfers of reward, under pre-specified conditions. Our contributions are theoretical and empirical. First, we show that this augmentation makes all subgame-perfect equilibria of all fully observed Markov games exhibit socially optimal behavior, given a sufficiently rich space of contracts. Next, we complement our game-theoretic analysis by showing that state-of-the-art RL algorithms learn socially optimal policies given our augmentation. Our experiments include classic static dilemmas like Stag Hunt, Prisoner's Dilemma and a public goods game, as well as dynamic interactions that simulate traffic, pollution management and common pool resource management.
    Date: 2022–08
  5. By: Rangeet Bhattacharyya; Palash Dey; Swaprava Nath
    Abstract: The auction of a single indivisible item is one of the most celebrated problems in mechanism design with transfers. Despite its simplicity, it provides arguably the cleanest and most insightful results in the literature. When the information of the auction is available to every participant, Myerson [17] provided a seminal result to characterize the incentive-compatible auctions along with revenue optimality. However, such a result does not hold in an auction on a network, where the information of the auction is spread via the agents, and they need incentives to forward the information. In recent times, a few auctions (e.g., [10, 15]) were designed that appropriately incentivize the intermediate nodes on the network to promulgate the information to potentially more valuable bidders. In this paper, we provide a Myerson-like characterization of incentive-compatible auctions on a network and show that the currently known auctions fall within this larger class of randomized auctions. We obtain the structure of the revenue optimal auction for i.i.d. bidders on arbitrary trees. We discuss the possibilities of addressing more general settings. Through experiments, we show that auctions following this characterization can provide a higher revenue than the currently known auctions on networks.
    Date: 2022–08
  6. By: Ali Hortaçsu; Aniko Oery; Kevin R. Williams
    Abstract: We introduce a model of oligopoly dynamic pricing where firms with limited capacity face a sales deadline. We establish conditions under which the equilibrium is unique and converges to a system of differential equations. Using unique and comprehensive pricing and bookings data for competing U.S. airlines, we estimate our model and find that dynamic pricing results in higher output but lower welfare than under uniform pricing. Our theoretical and empirical findings run counter to standard results in single-firm settings due to the strategic role of competitor scarcity. Pricing heuristics commonly used by airlines increase welfare relative to estimated equilibrium predictions.
    JEL: C70 C73 D21 D22 D43 D60 L13 L93
    Date: 2022–08
  7. By: Antelo, Manel; Bru, Lluís
    Abstract: In a differentiated Stackelberg duopoly, we explore the licensing behaviour of an inside patent holder owning a cost-reducing innovation and that may play as a leader or follower in setting the output level in the marketplace. We find that, regardless of whether the licensor is the leader or the follower, the licensing contract always involves royalties: per-unit or ad-valorem (depending on the degree of product differentiation and the size of the innovation) when the licensor is the leading firm, and per-unit royalties (alone or combined with a fixed payment) when it is the follower. We also show that, as compared to the pre-licensing context, licensing by a market follower is never welfare reducing, and licensing by a market leader is only welfare reducing when the products are very close substitutes.
    Keywords: Stackelberg industry, licensing, differentiated products, per-unit and ad-valorem royalties, welfare
    JEL: L13 L24
    Date: 2022–04

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