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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:ces:ceswps:_11686 |
| By: | Peter Achim; Jan Knoepfle |
| Abstract: | A principal continually decides whether to approve resource allocations to an agent, who exerts private effort to remain eligible. The principal must perform costly inspections to determine the agent's eligibility. We characterize Markov Perfect Equilibria and analyze the paths of trust and oversight that emerge from the dynamic interplay of effort and oversight. At high trust levels, effort is an intertemporal substitute to oversight, which leads to unique interior effort choices and random inspections. At low trust levels, effort is an intertemporal complement to oversight, which may create a coordination problem, leading to equilibrium multiplicity. Voluntary disclosure can mitigate this coordination issue. |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2504.02696 |
| By: | Mario Ghossoub; Bin Li; Benxuan Shi |
| Abstract: | We consider a monopoly insurance market with a risk-neutral profit-maximizing insurer and a consumer with Yaari Dual Utility preferences that distort the given continuous loss distribution. The insurer observes the loss distribution but not the risk attitude of the consumer, proxied by a distortion function drawn from a continuum of types. We characterize the profit-maximizing, incentive-compatible, and individually rational menus of insurance contracts, show that equilibria are separating, and provide key properties thereof. Notably, insurance coverage and premia are monotone in the level of risk aversion; the most risk-averse consumer receives full insurance $(\textit{efficiency at the top})$; the monopoly absorbs all surplus from the least-risk averse consumer; and consumers with a higher level of risk aversion induce a higher expected profit for the insurer. Under certain regularity conditions, equilibrium contracts can be characterized in terms of the marginal loss retention per type of consumer, and they consist of menus of layered deductible contracts, where each such layered structure is determined by the risk type of the consumer. In addition, we examine the effect of a fixed insurance provision cost on equilibria. We show that if the fixed cost is prohibitively high, then there will be no $\textit{ex ante}$ gains from trade. However, when trade occurs, separating equilibrium contracts always outperform pooling equilibrium contracts, and they are identical to those obtained in the absence of fixed costs, with the exception that only part of the menu is excluded. The excluded contracts are those designed for consumers with relatively lower risk aversion, who are less valuable to the insurer. Finally, we characterize incentive-efficient menus of contracts in the context of an arbitrary type space. |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2504.01095 |
| By: | Yiding Feng; Wei Tang |
| Abstract: | We introduce and study the persuasive calibration problem, where a principal aims to provide trustworthy predictions about underlying events to a downstream agent to make desired decisions. We adopt the standard calibration framework that regulates predictions to be unbiased conditional on their own value, and thus, they can reliably be interpreted at the face value by the agent. Allowing a small calibration error budget, we aim to answer the following question: what is and how to compute the optimal predictor under this calibration error budget, especially when there exists incentive misalignment between the principal and the agent? We focus on standard Lt-norm Expected Calibration Error (ECE) metric. We develop a general framework by viewing predictors as post-processed versions of perfectly calibrated predictors. Using this framework, we first characterize the structure of the optimal predictor. Specifically, when the principal's utility is event-independent and for L1-norm ECE, we show: (1) the optimal predictor is over-(resp. under-) confident for high (resp. low) true expected outcomes, while remaining perfectly calibrated in the middle; (2) the miscalibrated predictions exhibit a collinearity structure with the principal's utility function. On the algorithmic side, we provide a FPTAS for computing approximately optimal predictor for general principal utility and general Lt-norm ECE. Moreover, for the L1- and L-Infinity-norm ECE, we provide polynomial-time algorithms that compute the exact optimal predictor. |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2504.03211 |
| By: | Sebastian Schweighofer-Kodritsch; Roland Strausz |
| Abstract: | Casting mechanism design with evidence in the framework of Myerson (1982) implies that his generalized revelation principle directly applies, and we thus obtain standard notions of incentive compatible direct mechanisms. Their specific nature depends, however, on whether the presentation of evidence is controllable contractually. For deterministic implementation, we show that, in general, such control has value. We identify two independent conditions under which this value vanishes, one on evidence (WET) and another on preferences (TIWO). Allowing for fully stochastic mechanisms, we also characterize the (limited) extent to which the common assumption of evidentiary normality (NOR) negates any value of randomization. When NOR holds together with WET or TIWO, neither control nor randomization has any value. Many mechanism design settings satisfy these conditions naturally, implying that they are highly tractable. |
| Keywords: | mechanism design, revelation principle, evidence, verifiable iInformation, value of control, value of randomization. |
| JEL: | D82 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_11794 |