Strategy-proof allocation with outside option

TL;DR

This paper studies strategy-proof mechanisms in allocation problems with outside options, providing a unified foundation for existing results and new insights into mechanism equivalence and agent outside option probabilities.

Contribution

It offers a unified theoretical framework for strategy-proof mechanisms with outside options, including conditions for mechanism equivalence and agent outside option probabilities.

Findings

Pinning outside option probabilities characterizes mechanisms.

A sufficient condition for mechanism equivalence when allocations are finite.

Unifies and extends existing results in various models.

Abstract

Strategy-proof mechanisms are widely used in market design. In an abstract allocation framework where outside options are available to agents, we obtain two results for strategy-proof mechanisms. They provide a unified foundation for several existing results in distinct models and imply new results in some models. The first result proves that, for individually rational and strategy-proof mechanisms, pinning down every agent's probability of choosing his outside option is equivalent to pinning down a mechanism. The second result provides a sufficient condition for two strategy-proof mechanisms to be equivalent when the number of possible allocations is finite.