A Pseudo-Market Approach to Allocation with Priorities

Abstract

We propose a pseudo-market mechanism for no-monetary-transfer allocation of indivisible objects based on priorities such as those in school choice. Agents are given token money, face priority-specific prices, and buy utility-maximizing random assignments. The mechanism is asymptotically incentive compatible, and the resulting assignments are fair and constrained Pareto efficient. Hylland and Zeckhauser’s (1979) position-allocation problem is a special case of our framework, and our results on incentives and fairness are also new in their classical setting. (JEL D63, D82, H75, I21, I28)

A note on ex-ante stable lotteries

“…For the classical marriage model the condition was first considered by Roth et al (1993). He et al (2017) define an appealing class of mechanisms that implement ex-ante stable lotteries.…”

Welfare Theorems for Random Assignments with Priorities

“…The main technical difficulty in their proof, in comparison to the classical welfare theorems for exchange economies, is that in the context of lotteries one necessarily deals with satiated preferences (since probabilities have to add up to 1, respectively since each applicants receives at most one school seat). We show that the result does not generalize to the markets with priority-specific pricing of He et al (2017).…”

“…Kesten andÜnver (2015) consider mechanisms that implement ex-ante stable assignments and satisfy constrained ordinal efficiency properties. He et al (2017) define an appealing class of mechanisms that implement ex-ante stable lotteries. These mechanisms generalize the pseudo-market mechanisms of Hylland and Zeckhauser (1979) by allowing for priority-specific pricing (agents with different priorities are offered different prices).…”

“…In this section, we consider the pseudo-markets with priority-specific pricing of He et al (2017). A random assignment is generated by a pseudo-market of probability shares.…”

“…We also consider cardinal welfare theorems (for the difference between cardinal and ordinal welfare theorems see the discussion below) and show by means of a counter example that a cardinal second welfare cannot be established for our constrained efficiency notion in the context of the pseudo markets of He et al (2017).…”