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on Contract Theory and Applications |
| By: | Luca Di Corato (Department of Economics, Ca Foscari University of Venice); Michele Moretto (Department of Economics and Management, University of Padova, Fondazione Eni Enrico Mattei and Centro Studi Levi-Case) |
| Abstract: | We consider a long-term contractual relationship in which a buyer procures a fixed quantity of a product from a supplier and then sells it on the market. The production cost is private information and evolves randomly over time. The solution to this dynamic principal-agent problem involves a periodic two-part payment. The fixed part of the payment depends on the initial supplier’s cost type while the other is contingent on the current cost type. A notable feature is that, by using the information about the initial cost type, the buyer can reduce the burden of information rents paid for the revelation of the future cost type. We show that the distortion, resulting from information asymmetry, remains constant over time and decreases with the initial type. Lastly, we show that our analysis immediately applies also when input prices are private information and evolve randomly over time. |
| Keywords: | Dynamic Principal-Agent model, Supply contracting, Continuous time, Two-part payment |
| JEL: | C61 D82 D86 |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2024.04&r=cta |
| By: | Sumit Goel; Wade Hann-Caruthers |
| Abstract: | We study a contract design problem between a principal and multiple agents. Each agent participates in an independent task with binary outcomes (success or failure), in which it may exert costly effort towards improving its probability of success, and the principal has a fixed budget which it can use to provide outcome-dependent rewards to the agents. Crucially, we assume the principal cares only about maximizing the agents' probabilities of success, not how much of the budget it expends. We first show that a contract is optimal for some objective if and only if it is a successful-get-everything contract. An immediate consequence of this result is that piece-rate contracts and bonus-pool contracts are never optimal in this setting. We then show that for any objective, there is an optimal priority-based weighted contract, which assigns positive weights and priority levels to the agents, and splits the budget among the highest-priority successful agents, with each such agent receiving a fraction of the budget proportional to her weight. This result provides a significant reduction in the dimensionality of the principal's optimal contract design problem and gives an interpretable and easily implementable optimal contract. Finally, we discuss an application of our results to the design of optimal contracts with two agents and quadratic costs. In this context, we find that the optimal contract assigns a higher weight to the agent whose success it values more, irrespective of the heterogeneity in the agents' cost parameters. This suggests that the structure of the optimal contract depends primarily on the bias in the principal's objective and is, to some extent, robust to the heterogeneity in the agents' cost functions. |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.15890&r=cta |
| By: | Francesc Dilmé |
| Abstract: | This paper studies bargaining between a seller and a buyer with binary private valuation. Because the setting is more tractable than the case of general valuation distributions (studied in Gul et al., 1986), we are able to explicitly construct the full set of equilibria via induction. This lets us provide a simple proof of the Coase conjecture and obtain new results: The seller extracts all surplus as she becomes more patient, and the equilibrium outcome converges to the perfect-information outcome as private information vanishes. We also fully characterize the case where there is a deadline: We establish that if the probability that the buyer’s valuation is high is large enough, then the seller charges a high price at all times, there are trade bursts at the outset and the deadline, and trade occurs at a constant rate in between. |
| Keywords: | Bargaining, private information, one-sided offers. |
| JEL: | C78 D82 |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2024_515&r=cta |
| By: | Rupayan Pal (Indira Gandhi Institute of Development Research); Emmanuel Petrakis (Departamento de Econom¡a, Universidad Carlos III de Madrid) |
| Abstract: | This paper shows that in a duopoly a firm has no incentives to divest its passive shares in its rival when firms' strategies are strategic complements. This holds independently whether goods are substitutes or complements and whether firms engage in simultaneous or sequential move product market competition. However, if firms' strategies are strategic substitutes and are engaged in simultaneous move competition, it is optimal for both firms to fully divest their shares in their rivals under a private placement mechanism via independent intermediaries or under competitive bidding. Yet, in the sequential move game only the follower has such incentives. Notably, under a private placement mechanism via a common intermediary, there are circumstances under which there are partial or no firms' divestment incentives, highlighting that the divestment mechanism employed by firms may have a crucial role on their divestment incentives. |
| Keywords: | Cross-ownership, passive shares, strategic substitutes and complements, divestment incentives, market competition |
| JEL: | L13 L41 L2 D43 |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:ind:igiwpp:2024-003&r=cta |