Delegated Pandora's box
Curtis Bechtel, Shaddin Dughmi, Neel Patel

TL;DR
This paper investigates the delegation gap in generalized Pandora's box problems, analyzing how delegation affects the principal's utility under various models and constraints, and identifying conditions for constant-factor bounds.
Contribution
It introduces new models and bounds for delegation gaps in Pandora's box problems, including the free-agent, discounted-cost, and shared-cost variants, under different constraints.
Findings
Constant-factor delegation gaps exist for binary support variables with matroid constraints.
No constant-factor delegation gap exists for non-binary instances of the problem.
Shared-cost model achieves constant delegation gaps for certain downward closed constraints.
Abstract
In delegation problems, a principal does not have the resources necessary to complete a particular task, so they delegate the task to an untrusted agent whose interests may differ from their own. Given any family of such problems and space of mechanisms for the principal to choose from, the delegation gap is the worst-case ratio of the principal's optimal utility when they delegate versus their optimal utility when solving the problem on their own. In this work, we consider the delegation gap of the generalized Pandora's box problem, a search problem in which searching for solutions incurs known costs and solutions are restricted by some downward-closed constraint. First, we show that there is a special case when all random variables have binary support for which there exist constant-factor delegation gaps for matroid constraints. However, there is no constant-factor delegation gap for…
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