Abstract
We consider a principal who allocates an indivisible object among a finite number of agents who arrive on-line, each of whom prefers to have the object than not. Each agent has access to private information about the principal’s payoff if he receives the object. The decision to allocate the object to an agent must be made upon arrival of an agent and is irreversible. There are no monetary transfers but the principal can verify agents’ reports at a cost and punish them. A novelty of this paper is a reformulation of this on-line problem as a compact linear program. Using the formulation we characterize the form of the optimal mechanism and reduce the on-line version of the verification problem with identical distributions to an instance of the secretary problem with one fewer secretary and a modified value distribution. This reduction also allows us to derive a prophet inequality for the on-line version of the verification problem.
Research supported in part by DARPA grant HR001118S0045.
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Notes
- 1.
This result does not assume that the distribution of types is IID.
- 2.
We take verification cost and punishment level as exogenous but it is possible that the principal can get more precise information by incurring a higher information acquisition cost, which, in turn, leads to a more severe expected punishment. The results in this paper readily extend to the case where the principal can jointly optimize over verification cost and punishment level.
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Epitropou, M., Vohra, R. (2019). Optimal On-Line Allocation Rules with Verification. In: Fotakis, D., Markakis, E. (eds) Algorithmic Game Theory. SAGT 2019. Lecture Notes in Computer Science(), vol 11801. Springer, Cham. https://doi.org/10.1007/978-3-030-30473-7_1
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