The Machiavellian frontier of top trading cycles

TL;DR

This paper explores the top trading cycles rule in housing markets, weakening strategy-proofness to truncation-invariance, and provides new axiomatic characterizations that refine previous results.

Contribution

It introduces truncation-invariance as a weaker incentive notion and offers new characterizations of the TTC rule based on this concept.

Findings

Truncation-invariance prevents agents from altering outcomes through truncation misreports.

New axiomatic characterizations of TTC involve truncation-invariance combined with other properties.

Previous characterizations relying on strategy-proofness do not hold under truncation-invariance.

Abstract

This paper studies the housing market problem introduced by Shapley and Scarf (1974). We probe the Machiavellian frontier of the well-known top trading cycles (TTC) rule by weakening strategy-proofness and providing new characterizations for this rule. Specifically, our contribution lies in three aspects. First, we weaken the concept of strategy-proofness and introduce a new incentive notion called truncation-invariance, where the truthful preference-reporting assignment cannot be altered by any agent through misreporting a truncation of the true preference at the assignment produced by the true preference unilaterally. Second, we characterize the TTC rule by the following three groups of axioms: individual rationality, pair-efficiency, truncation-invariance; individual rationality, Pareto efficiency, truncation-invariance; individual rationality, endowments-swapping-proofness, truncation-invariance.1 The new characterizations refine several previous results.2 Third, we show through examples that the characterization results of Takamiya (2001) and Miyagawa (2002) can no longer be obtained if strategy-proofness is replaced with truncation-invariance.