Mechanism Design with Exchangeable Allocations

TL;DR

This paper explores mechanism design without payments for agents with diverse preferences, introducing exchange phases to improve social welfare, and provides mechanisms for both centralized and individual exchanges.

Contribution

It introduces exchange phases into mechanism design without payments for diverse preferences and develops mechanisms that optimize or approximate social welfare.

Findings

A truthful mechanism for central exchanges that optimizes social welfare.

A universally truthful randomized mechanism achieving at least half of the optimal welfare in individual exchanges.

Demonstrates limitations of traditional mechanisms without payments with diverse preferences.

Abstract

We investigate mechanism design without payments when agents have different types of preferences. Contrary to most settings in the literature where agents have the same preference, e.g. in the facility location games all agents would like to stay close to (or away from) the facility, we demonstrate the limitation of mechanism design without payments when agents have different preferences by introducing exchanging phases. We consider two types of exchanging phases. The first model is called central exchanges where the exchanges are performed by a central authority. The other model is called individual exchanges where agents exchange their outcomes by themselves. By using facility location games as an example, we provide a truthful mechanism that optimizes social welfare in central exchanges. We also provide a universally truthful randomized mechanism that achieves at least a half of the optimal social welfare in individual exchanges.