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on Contract Theory and Applications |
| By: | Alejandro Francetich; Burkhard C. Schipper (Department of Economics, University of California Davis) |
| 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. |
| Keywords: | Screening, discrete concave optimization, rationalizability, level-$k$ reasoning |
| JEL: | D82 |
| Date: | 2025–10–23 |
| URL: | https://d.repec.org/n?u=RePEc:cda:wpaper:375 |
| By: | Izgarshev, Mark; Lukyanov, Georgy |
| Abstract: | A benevolent advisor observes a project’s complexity and posts a pass–fail threshold before the agent chooses effort. The project suc-ceeds only if ability and effort together clear complexity. We com-pare two informational regimes. In the naive regime, the threshold is treated as non-informative; in the sophisticated regime, the threshold is a signal and the agent updates beliefs. We characterize equilibrium threshold policies and show that the optimal threshold rises with com-plexity under mild regularity. We then give primitives-based sufficient conditions that guarantee separating, pooling, or semi-separating out-comes. In a benchmark with uniform ability, exponential complexity, and power costs, we provide explicit parameter regions that partition the space by equilibrium type; a standard refinement eliminates most pooling. The results yield transparent comparative statics and welfare comparisons across regimes. |
| Keywords: | threshold tests; signaling; information design; monotone comparative statics; pooling vs. separation. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:tse:wpaper:131005 |
| By: | Lukyanov, Georgy; Shamruk, Konstantin; Logina, Ekaterina |
| Abstract: | We study a dynamic reputation model with a fixed posted price where only pur-chases are public. A long-lived seller chooses costly quality; each buyer observes the purchase history and a private signal. Under a Markov selection, beliefs split into two cascades—where actions are unresponsive and investment is zero—and an interior region where the seller invests. The policy is inverse-U in reputation and produces two patterns: Early Resolution (rapid absorption at the optimistic cascade) and Dou-ble Hump (two investment episodes). Higher signal precision at fixed prices enlarges cascades and can reduce investment. We compare welfare and analyze two design levers: flexible pricing, which can keep actions informative and remove cascades for patient sellers, and public outcome disclosure, which makes purchases more informa-tive and expands investment. |
| Keywords: | Reputation; Social learning; Informational cascades; Product quality; Dynamic games. |
| JEL: | D82 D83 C73 L15 |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:tse:wpaper:131019 |
| By: | Smolin, Alex; Yamashita, Takuro |
| Abstract: | We study information design in games where players choose from a continuum of ac-tions and have continuously differentiable payoffs. We show that an information structure is optimal when the equilibrium it induces can also be implemented in a principal-agent contracting problem. Building on this result, we characterize optimal information struc-tures in symmetric linear-quadratic games. With common values, targeted disclosure is robustly optimal across all priors. With interdependent and normally distributed values, linear disclosure is uniquely optimal. We illustrate our findings with applications in venture capital, Bayesian polarization, and price competition. |
| Keywords: | Bayesian persuasion; information design; dual certification; first-order approach; linear-quadratic games; targeted disclosure; Gaussian coupling, linea; disclosure. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:tse:wpaper:130998 |
| By: | Alejandro Francetich; Burkhard Schipper (Department of Economics, University of California Davis) |
| 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. |
| Keywords: | Screening, disclosure, unawareness, principal-agent model, rationalizability |
| JEL: | D83 |
| Date: | 2025–10–23 |
| URL: | https://d.repec.org/n?u=RePEc:cda:wpaper:374 |