# Strategyproof Multi-Item Exchange Under Single-Minded Dichotomous Preferences

## TL;DR

This paper introduces a condition called weak consistency that ensures strategyproof multi-item exchange mechanisms are robust under various constraints, with specific mechanisms satisfying optimality and rationality criteria.

## Contribution

It identifies weak consistency as a key condition for strategyproofness in multi-item exchanges and highlights mechanisms satisfying Pareto optimality and individual rationality.

## Key findings

- Weak consistency guarantees strategyproofness under diverse constraints.
- Two mechanisms achieve constrained Pareto optimality and strong individual rationality.
- Impossibility results for more permissive individual rationality settings.

## Abstract

We consider multi-item exchange markets in which agents want to receive one of their target bundles of resources. The model encompasses well-studied markets for kidney exchange, lung exchange, and multi-organ exchange. We identify a general and sufficient condition called weak consistency for the exchange mechanisms to be strategyproof even if we impose any kind of distributional, diversity, or exchange cycle constraints. Within the class of weakly consistent and strategyproof mechanisms, we highlight two important ones that satisfy constrained Pareto optimality and strong individual rationality. Several results in the literature follow from our insights. We also derive impossibility results when constrained Pareto optimality is defined with respect to more permissive individual rationality requirements.