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on Contract Theory and Applications |
| By: | David Bardey; Philippe De Donder; Marie-Louise Leroux |
| Abstract: | We study a situation where physicians differing in their degree of altruism exert a diagnostic effort before deciding whether to test patients to determine the most appropriate treatment. The diagnostic effort generates an imperfect private signal of the patient’s type, while the test is perfect. At the laissez-faire, physicians exert insufficient diagnostic effort and rely excessively on testing. We show that the first-best allocation (where the degree of altruism is observable) can be decentralized by a payment scheme composed of i) a pay-for-performance (P4P) part based on the number of correctly treated patients to ensure the provision of the optimal diagnostic effort, and of ii) a capitation part to ensure both the optimal testing decision and the participation of physicians. When physicians differ in their (non-observable) degree of altruism, the optimal contract is pooling rather than separating, an instance of non-responsiveness. Its uniform P4P component induces more altruistic physicians to exert a larger diagnostic effort while, to incentivize the second-best optimal testing decision, its capitation component must be contingent on the test cost. |
| Keywords: | diagnostic risk, personalized medicine, non-responsiveness, capitation payment, pay-for-performance, hidden action and hidden information. |
| JEL: | D82 D86 I18 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:rsi:creeic:2501 |
| By: | Paul Duetting; Michal Feldman; Tomasz Ponitka; Ermis Soumalias |
| Abstract: | Algorithmic contract design studies scenarios where a principal incentivizes an agent to exert effort on her behalf. In this work, we focus on settings where the agent's type is drawn from an unknown distribution, and formalize an offline learning framework for learning near-optimal contracts from sample agent types. A central tool in our analysis is the notion of pseudo-dimension from statistical learning theory. Beyond its role in establishing upper bounds on the sample complexity, pseudo-dimension measures the intrinsic complexity of a class of contracts, offering a new perspective on the tradeoffs between simplicity and optimality in contract design. Our main results provide essentially optimal tradeoffs between pseudo-dimension and representation error (defined as the loss in principal's utility) with respect to linear and bounded contracts. Using these tradeoffs, we derive sample- and time-efficient learning algorithms, and demonstrate their near-optimality by providing almost matching lower bounds on the sample complexity. Conversely, for unbounded contracts, we prove an impossibility result showing that no learning algorithm exists. Finally, we extend our techniques in three important ways. First, we provide refined pseudo-dimension and sample complexity guarantees for the combinatorial actions model, revealing a novel connection between the number of critical values and sample complexity. Second, we extend our results to menus of contracts, showing that their pseudo-dimension scales linearly with the menu size. Third, we adapt our algorithms to the online learning setting, where we show that, a polynomial number of type samples suffice to learn near-optimal bounded contracts. Combined with prior work, this establishes a formal separation between expert advice and bandit feedback for this setting. |
| Date: | 2025–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2501.14474 |
| By: | Deniz Kattwinkel; Justus Preusser |
| Abstract: | A surplus must be divided between a principal and an agent. Only the agent knows the surplus' true size and decides how much of it to reveal initially. Both parties can exert costly effort to conclusively prove the surplus' true size. The agent's liability is bounded by the revealed surplus. The principal is equipped with additional funds. The principal designs a mechanism that allocates the burden of proof and divides the surplus. In principal-optimal mechanisms, the principal's effort to acquire proof decreases in the revealed surplus. The agent's effort initially decreases, but then the sign of its slope alternates across five intervals. Applications include wealth taxation, corporate finance, and public procurements. |
| Date: | 2025–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2501.14686 |
| By: | David Bardey; Philippe De Donder; Marie-Louise Leroux |
| Abstract: | In this paper, the authors study the following : Doctors with different levels of altruism put in varying amounts of effort to diagnose patients before deciding on tests. The diagnostic effort gives an imperfect idea of the patient's condition, while tests are perfect. Without regulation, doctors don't put in enough diagnostic effort and rely too much on tests. The optimal outcome can be achieved with a payment system that includes: Pay-for-performance (P4P) based on correctly treated patients to encourage proper diagnostic effort. Capitation to ensure the right testing decisions and doctor participation. When doctors' altruism levels cannot be observed, a uniform P4P component encourages more altruistic doctors to make more diagnostic efforts. The capitation part should depend on test costs to motivate the optimal testing decisions. Dans ce cahier, les auteurs étudient les éléments suivants : les médecins avec différents niveaux d'altruisme exercent des efforts variables pour diagnostiquer leurs patients avant de décider de leur faire passer éventuellement un test. L'effort de diagnostic donne une idée imparfaite de l'état du patient, tandis que les tests sont parfaits. Sans régulation, les médecins n’exercent pas assez d'effort de diagnostic et utilisent trop souvent les tests. Le résultat optimal en termes d’effort et de tests peut être obtenu avec un système de paiement qui inclut : Un Paiement à la performance (P4P) basé sur les patients correctement traités pour encourager un effort de diagnostic approprié. Un paiement par capitation pour assurer les bonnes décisions de test et la participation des médecins. Lorsque les niveaux d'altruisme des médecins ne sont pas observables, une partie P4P uniforme encourage les médecins plus altruistes à faire plus d’effort de diagnostic. La capitation doit dépendre des coûts des tests pour motiver les décisions optimales de test. |
| Keywords: | diagnostic risk, personalized medicine, non-responsiveness, capitation payment, pay-for-performance, hidden action and hidden information, risque de diagnostic, médecine personnalisée, non-réponse, paiement par capitation, paiement à la performance, action cachée et information cachée |
| JEL: | D82 D86 I18 |
| Date: | 2025–02–03 |
| URL: | https://d.repec.org/n?u=RePEc:cir:cirwor:2025s-02 |
| By: | Huisheng Wang; H. Vicky Zhao |
| Abstract: | In financial markets, agents often mutually influence each other's investment strategies and adjust their strategies to align with others. However, there is limited quantitative study of agents' investment strategies in such scenarios. In this work, we formulate the optimal investment differential game problem to study the mutual influence among agents. We derive the analytical solutions for agents' optimal strategies and propose a fast algorithm to find approximate solutions with low computational complexity. We theoretically analyze the impact of mutual influence on agents' optimal strategies and terminal wealth. When the mutual influence is strong and approaches infinity, we show that agents' optimal strategies converge to the asymptotic strategy. Furthermore, in general cases, we prove that agents' optimal strategies are linear combinations of the asymptotic strategy and their rational strategies without others' influence. We validate the performance of the fast algorithm and verify the correctness of our analysis using numerical experiments. This work is crucial to comprehend mutual influence among agents and design effective mechanisms to guide their strategies in financial markets. |
| Date: | 2025–01 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2501.14259 |