Theoretical Economics, Volume 17, Number 3 ( 2022)

Theoretical Economics 17 (2022), 1109–1143

Prior-free dynamic allocation under limited liability

Sylvain Chassang, Samuel Kapon


A principal seeks to efficiently allocate a productive public resource to a number of possible users. Vickrey-Clarke-Groves (VCG) mechanisms provide a detail-free way to do so provided users have deep pockets. In practice however, users may have limited resources. We study a dynamic allocation problem in which participants have limited liability: transfers are made ex post, and only if the productive efforts of participants are successful. We show that it is possible to approximate the performance of the pivot VCG mechanism using limited liability detail-free mechanisms that selectively ignore reports from participants who cannot make their promised payments. A complementary use of cautiousness and forgiveness achieves approximate renegotiation-proofness. We emphasize the use of prior-free online optimization techniques to approximate aggregate incentive properties of the pivot mechanism.

Keywords: Dynamic allocation, renegotiation-proofness, lending, limited liability, VCG, approachability, online optimization, cautiousness, forgiveness

JEL classification: D82

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