Minimally rational reallocation of objects

2026-09-23

AI Summary

本文通过个体理性、配对理性和策略性证明三个弱理性公理，解决了对象再分配问题，并表明这些公理唯一确定了TTC方法。

Abstract

Matching theory has largely evolved around two canonical rules: deferred acceptance (DA) in the marriage problem and top trading cycles (TTC) in the object reallocation problem. Although the two rules operate through different procedures, we show that they rest on a common axiomatic foundation. In the marriage problem, stability decomposes into individual rationality and pair rationality, and a classic result characterizes DA by these two axioms together with strategy-proofness for the proposing side. We show that individual rationality, pair rationality, and strategy-proofness likewise characterize TTC. More strongly, three weak rationality axioms concerning individuals and pairs, together with strategy-proofness, uniquely determine TTC. Even weak rationality requirements therefore rule out strategy-proof implementation when there is a cap on the size of exchange cycles.

Problem

• matching theory
• strategy-proofness
• rationality axioms
• object reallocation

Innovation

• top trading cycles
• deferred acceptance
• strategy-proofness