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on Contract Theory and Applications |
| By: | Alejandro Francetich; Burkhard C. Schipper |
| Abstract: | We consider a principal who wishes to screen an agent with \emph{discrete} types by offering a menu of \emph{discrete} quantities and \emph{discrete} transfers. We assume that the principal's valuation is discrete strictly concave and use a discrete first-order approach. We model the agent's cost types as non-integer, with integer types as a limit case. Our modeling of cost types allows us to replicate the typical constraint-simplification results and thus to emulate the well-treaded steps of screening under a continuum of contracts. We show that the solutions to the discrete F.O.C.s need not be unique \textit{even under discrete strict concavity}, but we also show that there cannot be more than two optimal contract quantities for each type, and that -- if there are two -- they must be adjacent. Moreover, we can only ensure weak monotonicity of the quantities \textit{even if virtual costs are strictly monotone}, unless we limit the ``degree of concavity'' of the principal's utility. Our discrete screening approach facilitates the use of rationalizability to solve the screening problem. We introduce a rationalizability notion featuring robustness with respect to an open set of beliefs over types called \textit{$\Delta$-O Rationalizability}, and show that the set of $\Delta$-O rationalizable menus coincides with the set of usual optimal contracts -- possibly augmented to include irrelevant contracts. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2510.20921 |
| By: | Heng-fu Zou (Institute for Advanced Study, Wuhan University) |
| Abstract: | This paper develops a continuous-time model of contracting between a principal and many agents under moral hazard, linking dynamic contract theory to the mean field game (MFG) framework. Outputs depend on effort, competition, and both idiosyncratic and common shocks. The principal designs contracts using filtered signals that benchmark agents against peers. We show that the first-order approach remains valid: effort is linear in exposure with slope determined by the informativeness of filtered outputs. The Hamilton-Jacobi-Bellman equation implies that optimal incentives depend jointly on marginal revenue, signal variance, and intertemporal insurance. The optimal filter is the generalized least squares residual, which asymptotically eliminates common shocks as group size grows. In a linear-quadratic specialization, equilibrium exists, is unique, and is globally stable, with the uniqueness result coinciding with the Lasry-Lions MFG fixed-point condition. The framework unifies tournaments, RPE, and dynamic contracts, and explains empirical puzzles in executive pay, sales teams, and finance. |
| Date: | 2025–10–22 |
| URL: | https://d.repec.org/n?u=RePEc:cuf:wpaper:797 |
| By: | Roberto Corrao; Joel P. Flynn; Karthik Sastry |
| Abstract: | We introduce a model of incentive contracting in which the principal, in addition to writing contracts, must engage in contractibility design: creating an evidence structure that allows them to prove when the agent has breached the contract. Designing an evidence structure entails both (i) front-end costs borne ex ante, such as those of drafting contracts, and (ii) back-end costs borne ex post, such as those of generating evidence. We find that, under even small front-end costs, optimal contracts are coarse, specifying finitely many contingencies out of a continuum of possibilities. In contrast, under even large back-end costs, optimal contracts are complete. Applied to the design of procurement contracts, our results rationalize: (i) the discreteness of contracts, (ii) the presence of similarly vague contracts in low-stakes and high-stakes settings, and (iii) the discontinuous adjustment of contracts to changes in the economic environment. |
| JEL: | D82 D86 K0 |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:34379 |
| By: | Alejandro Francetich; Burkhard C. Schipper |
| Abstract: | We analyze a principal-agent procurement problem in which the principal (she) is unaware some of the marginal cost types of the agent (he). Communication arises naturally as some types of the agent may have an incentive to raise the principal's awareness (totally or partially) before a contract menu is offered. The resulting menu must not only reflect the principal's change in awareness, but also her learning about types from the agent's decision to raise her awareness in the first place. We capture this reasoning in a discrete concave model via a rationalizability procedure in which marginal beliefs over types are restricted to log-concavity, ``reverse'' Bayesianism, and mild assumptions of caution. We show that if the principal is ex ante only unaware of high-cost types, all of these types have an incentive raise her awareness of them -- otherwise, they would not be served. With three types, the two lower-cost types that the principal is initially aware of also want to raise her awareness of the high-cost type: Their quantities suffer no additional distortions and they both earn an extra information rent. Intuitively, the presence of an even higher cost type makes the original two look better. With more than three types, we show that this intuition may break down for types of whom the principal is initially aware of so that raising the principal's awareness could cease to be profitable for those types. When the principal is ex ante only unaware of more efficient (low-cost) types, then \textit{no type} raises her awareness, leaving her none the wiser. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2510.20918 |
| By: | Flora C. Shi; Martin J. Wainwright; Stephen Bates |
| Abstract: | We study hypothesis testing over a heterogeneous population of strategic agents with private information. Any single test applied uniformly across the population yields statistical error that is sub-optimal relative to the performance of an oracle given access to the private information. We show how it is possible to design menus of statistical contracts that pair type-optimal tests with payoff structures, inducing agents to self-select according to their private information. This separating menu elicits agent types and enables the principal to match the oracle performance even without a priori knowledge of the agent type. Our main result fully characterizes the collection of all separating menus that are instance-adaptive, matching oracle performance for an arbitrary population of heterogeneous agents. We identify designs where information elicitation is essentially costless, requiring negligible additional expense relative to a single-test benchmark, while improving statistical performance. Our work establishes a connection between proper scoring rules and menu design, showing how the structure of the hypothesis test constrains the elicitable information. Numerical examples illustrate the geometry of separating menus and the improvements they deliver in error trade-offs. Overall, our results connect statistical decision theory with mechanism design, demonstrating how heterogeneity and strategic participation can be harnessed to improve efficiency in hypothesis testing. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2510.21178 |
| By: | Schmitz, Patrick W. |
| Abstract: | We develop an incomplete-contracting model in which the government engages a private contractor to provide a public good. Over time, adaptations of the good to changing circumstances may become desirable. The contractor privately learns the costs of implementing these adaptations. We compare two organizational forms. In a public-private partnership, the government actively participates in project management and, by incurring information-gathering costs, may ascertain the contractor's adaptation costs. Under traditional procurement, the government lacks direct involvement in project management, preventing it from ascertaining the adaptation costs. We show that the government's potentially enhanced access to the contractor's information in a public-private partnership can either support or undermine the case for such partnerships. |
| Keywords: | public-private partnerships; traditional procurement; asymmetric information; incomplete contracts; information gathering |
| JEL: | D23 D86 H41 H57 L33 |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:126368 |