Ordinal Bayesian incentive compatibility in random assignment model

TL;DR

This paper investigates the concept of ordinal Bayesian incentive compatibility (OBIC) in the random assignment model, showing that under certain conditions, OBIC mechanisms are closely related to strategy-proofness, and strengthening existing impossibility results.

Contribution

It introduces a robust version of OBIC and proves that locally robust OBIC mechanisms with elementary monotonicity are strategy-proof, extending the understanding of incentive compatibility.

Findings

Large class of mechanisms are OBIC with uniform prior

Locally robust OBIC mechanisms with elementary monotonicity are strategy-proof

No locally robust OBIC and ordinally efficient mechanism exists with at least four agents

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.