Ordinal Bayesian incentive compatibility in random assignment model
Abstract
We explore the consequences of weakening the notion of incentive compatibility from strategy-proofness to ordinal Bayesian incentive compatibility (OBIC) in the random assignment model. If the common prior of the agents is a uniform prior, then a large class of random mechanisms are OBIC with respect to this prior -- this includes the probabilistic serial mechanism. We then introduce a robust version of OBIC: a mechanism is locally robust OBIC if it is OBIC with respect all independent priors in some neighborhood of a given independent prior. We show that every locally robust OBIC mechanism satisfying a mild property called elementary monotonicity is strategy-proof. This leads to a strengthening of the impossibility result in Bogomolnaia and Moulin (2001): if there are at least four agents, there is no locally robust OBIC and ordinally efficient mechanism satisfying equal treatment of equals.
Cite
@article{arxiv.2009.13104,
title = {Ordinal Bayesian incentive compatibility in random assignment model},
author = {Sulagna Dasgupta and Debasis Mishra},
journal= {arXiv preprint arXiv:2009.13104},
year = {2022}
}