Generalized Partition Mechanism: Framework for Combining Multiple Strategy-Proof Mechanisms

This paper presents a framework for combining multiple strategy-proof resource allocation mechanisms, in which participants are divided into several groups (partitions) and each mechanism is applied to one partition. The idea of dividing participants into several groups is introduced to achieve budget balance in a redistribution mechanism, i.e., the payment (money) collected in one partition is distributed in another partition. Furthermore, this idea has been used to adjust parameters of a mechanism (e.g., the reservation price in an auction) based on the information of participants in one partition in order to improve the mechanism's efficiency or revenue. This paper presents a unified framework called a generalized partition mechanism, in which information, money, and unsold goods can be transferred among partitions. This framework is very general and thus can be applied to various settings, including cases where a redistribution mechanism must adjust parameters to obtain a better social surplus. We provide a sufficient condition on the flow of information, money, and goods among partitions so that the generalized partition mechanism is strategy-proof, assuming that each mechanism applied to the partition is strategy-proof. We can use this sufficient condition as a guideline for combining multiple mechanisms. To show the applicability of this guideline, we develop new redistribution mechanisms based on this guideline, in which the utility of a participant can be non-quasi-linear.