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On Incentives in Three-Sided Markets

Jorge Arenas and Juan Pablo Torres-Martínez

April 2024

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Abstract

In a class of three-sided matching problems that always have stable solutions, we show that no stable mechanism is strategy-proof for those who internalize the trilateral structure in their preferences. Furthermore, strong restrictions on preferences are needed to ensure that stability and one-sided strategy-proofness are compatible for all sides of the market. These results are related to the incompatibility between stability and one-sided group strategy-proofness in two-sided markets.

Preference rankings for agents in U over V and agents in V over W. Vertical dots leave remaining rankings unrestricted.Lexicographic preference rankings for agents in W: rankings of V on the left and U on the right.
Theorem 1. A three-sided market with four agents on each side in which no mechanism is both stable and strategy-proof for W. Agents in W rank V first and U second; dots denote arbitrary remaining rankings.