Designing Menus of Contracts Efficiently: The Power of Randomization
Matteo Castiglioni, Alberto Marchesi, Nicola Gatti

TL;DR
This paper demonstrates that in Bayesian principal-agent problems, designing menus of randomized contracts allows for near-optimal solutions to be computed efficiently, overcoming previous hardness results for deterministic menus.
Contribution
It introduces a polynomial-time algorithm for nearly optimal menus of randomized contracts, contrasting prior hardness results for deterministic menus, and refines analysis of deterministic contract menus.
Findings
Randomized contract menus enable polynomial-time near-optimal solutions.
Deterministic menus of contracts are APX-hard to optimize.
The principal's expected utility can be arbitrarily close to the supremum with randomized menus.
Abstract
We study hidden-action principal-agent problems in which a principal commits to an outcome-dependent payment scheme (called contract) so as to incentivize the agent to take a costly, unobservable action leading to favorable outcomes. In particular, we focus on Bayesian settings where the agent has private information. This is collectively encoded by the agent's type, which is unknown to the principal, but randomly drawn according to a finitely-supported, commonly-known probability distribution. In Bayesian principal-agent problems, the principal may be better off by committing to a menu of contracts specifying a contract for each agent's type, rather than committing to a single contract. This induces a two-stage process that resembles interactions studied in classical mechanism design: after the principal has committed to a menu, the agent first reports a type to the principal, and,…
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Taxonomy
TopicsAuction Theory and Applications · Consumer Market Behavior and Pricing · Law, Economics, and Judicial Systems
