- The paper's main contribution is a novel mechanism design framework where agents conceal part of their feasible actions, leading to a monotone envelope of promised utilities.
- The analysis introduces a bang-bang structure that segments type spaces into strictly increasing and constant utility intervals to satisfy incentive compatibility.
- Comparative statics demonstrate that while principal payoffs increase with technology-set expansions, agent utilities display ambiguous responses.
Screening for Choice Sets: Mechanism Design with Concealed Feasibility
This paper addresses a class of screening problems where the agent’s private information concerns which actions are feasible, rather than which parameters prevail in a known choice set. The principal knows the payoff consequences of actions but relies on the agent to disclose what is implementable. The agent can strategically conceal feasible technologies before the principal selects an action, fundamentally altering the attainable payoff set for the principal, even when types are observable. This notion deviates from classical Myersonian screening theory and better aligns with organizational, regulatory, and delegation settings where feasibility, rather than valuation, is privately known and verifiable ex post.
Central to tractability is the assumption that technology sets are ordered by set inclusion: more capable agents have access to strictly larger technology sets. The agent can only report subsets of their feasible set, and all reported technologies are verifiable. The principal can commit in advance to any rule mapping reported sets to actions in the induced choice set.
Mechanism Design Structure
The analysis decomposes the screening problem into two dimensions: (1) the principal’s promised utility function, specifying the agent's utility for any reported set, and (2) the selection of the principal's best attainable payoff for each report, consistent with the binding promised utility. The monotonicity constraint emerges from incentive compatibility: the promised utility must not decrease as the reported set grows, matching the intuition that higher capability cannot yield lower agent rent.
A significant innovation is the identification of a monotone envelope for promised utilities, constructed from the complete information payoff curve (i.e., the agent's equilibrium utility if the principal knows feasibility). For each reported set, the optimal promised utility is constrained to lie between the lower and upper monotone closures of the complete information curve. This envelope is sharp—any monotone function within it is feasible, and feasibility constraints cease to bind beyond this.
With observable types, the agent still retains private access to technologies and can threaten to report only the default technology. To discipline this, the optimal mechanism adopts a "shoot-the-agent" discipline, promising the minimal utility under the default technology to deviators. The equilibrium payoff for each type is the greater of their utility under the principal's optimal choice or their punishment utility, leading to potentially non-monotone complete information curves.
General Optimal Mechanism
When private information is present:
- Promised utility must be weakly increasing in capability.
- The feasible set of promised utilities collapses to the monotone envelope of the complete information curve.
- The principal optimizes her expected payoff by selecting a monotone promised utility within this envelope.
A central result is that the optimal mechanism exhibits a bang-bang structure: the type space is partitioned into intervals where the agent’s utility is either exactly the complete-information value (strictly increasing) or is held fixed (bunching). The number of constant (bunched) intervals is sharply bounded above by the number of strictly decreasing segments in the complete information curve, i.e., the number of local incentive reversals due to set-valued feasibility.
Comparative Statics and Implementation Properties
The paper establishes monotone comparative statics:
- Principal's expected payoff is strictly increasing under first-order stochastic dominance or under technology-set expansions, using a constructive coupling argument that respects the set-inclusion ordering.
- Agent’s payoff exhibits ambiguous comparative statics: while expanding default technologies always tightens discipline and reduces agent rents, capability improvements may reduce agent utility in regions requiring bunching to maintain incentive compatibility.
Moreover, any monotone, optimal-promised utility function fitting the described structure can be rationalized by varying either the distribution of capability types or the geometry of the choice sets, highlighting the model's flexibility despite its reduced-form tractability.
Applications
Persuasion Problems
Applications to Bayesian persuasion where senders control feasible experiments highlight the framework's relevance. Nested experiment sets enable tractable mechanism design for regulating information provision, with the monotone envelope structure determining reward sensitivity or compression in response to added persuasion power.
Action and Technology Delegation
The approach generalizes to action elicitation (e.g., policymakers screening for feasible reforms) and production-technology elicitation (e.g., boards screening CEOs for non-obvious strategies under moral hazard). In both, the monotone-envelope structure guides optimal compression of payoffs and under-exploitation of newly revealed options, depending on alignment between agent and principal payoffs.
Implications and Future Directions
This framework justifies institutional designs where reward differentiation is deliberately compressed in some capability ranges, and potentially superior options are underutilized—both are optimal responses to the peculiar incentive compatibility constraints imposed by private feasibility. The maximal number of "flat" regions in the optimal utility function is tightly bounded, tying the model’s complexity to observable features of the underlying complete-information payoff landscape.
The theoretical implications extend to robust institutional design under partial verifiability and to multidimensional screening environments where feasible sets, not valuations, are the agent’s private information. Practically, the results can inform regulations on project proposals, dynamic experimentation, and delegation contracts.
Several avenues remain open: relaxing the nested-set assumption, extending to dynamic environments with learning or breakthrough arrivals, and integrating limited commitment power.
Conclusion
This paper advances mechanism design by shifting private information from payoffs to feasibility, resolving high-dimensional tractability through the nested-set assumption and monotone-envelope characterization. The bang-bang structure of optimal policies highlights when and why institutions compress rewards and forego potential gains from incremental disclosures, providing a unified and tractable theory for screening where choice sets themselves are strategic variables.
Reference: "Screening for Choice Sets" (2601.15580)