Two-sided matching markets are ubiquitous in the real world, modeling scenarios such as ride-sharing platforms and college admissions. Stability and strategyproofness are two desirable properties in these systems, but are known to be incompatible.

This tutorial surveys the literature on strategic behavior in these markets, covering classical results and recent developments, with a focus on manipulations via preference misreports (where agents alter their ordinal rankings over potential matches) and capacity modifications (where agents misreport the number of agents they can be matched to).  Throughout, the tutorial will also highlight open problems and avenues for future work.

1. The Basics: The classical stable matching model, lattice results, and algorithms for computing stable solutions.

2. Models of strategic behavior: preference misreporting, capacity modification, etc.

3. Preference manipulation strategies 

   • One-sided manipulations: truncation and permutation strategies

   • Coalitional manipulation strategies: accomplice vs. self-manipulation strategies

   • One-sided coalitions, two-sided coalitions

4. Equilibria in strategic games

5. Capacity manipulation strategies

   • Making the case for capacity manipulation strategies

   • Capacity vs. preference manipulation strategies

   • Boundaries and possibilities

Coming soon!