Book contents
- Frontmatter
- Contents
- Acknowledgments
- Notations
- Introduction
- 1 The game of chess
- 2 Utility theory
- 3 Extensive-form games
- 4 Strategic-form games
- 5 Mixed strategies
- 6 Behavior strategies and Kuhn's Theorem
- 7 Equilibrium refinements
- 8 Correlated equilibria
- 9 Games with incomplete information and common priors
- 10 Games with incomplete information: the general model
- 11 The universal belief space
- 12 Auctions
- 13 Repeated games
- 14 Repeated games with vector payoffs
- 15 Bargaining games
- 16 Coalitional games with transferable utility
- 17 The core
- 18 The Shapley value
- 19 The bargaining set
- 20 The nucleolus
- 21 Social choice
- 22 Stable matching
- 23 Appendices
- References
- Index
22 - Stable matching
- Frontmatter
- Contents
- Acknowledgments
- Notations
- Introduction
- 1 The game of chess
- 2 Utility theory
- 3 Extensive-form games
- 4 Strategic-form games
- 5 Mixed strategies
- 6 Behavior strategies and Kuhn's Theorem
- 7 Equilibrium refinements
- 8 Correlated equilibria
- 9 Games with incomplete information and common priors
- 10 Games with incomplete information: the general model
- 11 The universal belief space
- 12 Auctions
- 13 Repeated games
- 14 Repeated games with vector payoffs
- 15 Bargaining games
- 16 Coalitional games with transferable utility
- 17 The core
- 18 The Shapley value
- 19 The bargaining set
- 20 The nucleolus
- 21 Social choice
- 22 Stable matching
- 23 Appendices
- References
- Index
Summary
Chapter summary
In this chapter we present the subject of stable matching. Introduced in 1962 by David Gale and Lloyd Shapley, stable matching became the starting point of a rich literature on matching problems in two-sided markets (e.g., workers and employers, interns and hospitals, students and universities), and remains one of the most applied areas in game theory to date.
We present Gale and Shapley's basic model of matching men to women, the concept of stable matching, and an algorithm for finding it. It is proved that the set of stable matchings has a lattice structure based on the preferences of women and men. We then study several variations of the model: the case in which there are more men than women; the case in which bachelorhood is not the worst outcome; the case of many-to-one matchings (e.g., many students to one college); and matchings in a single-gender population. It is also shown that the Gale–Shapley algorithm is not immune to strategic manipulations.
The study of the subject of this chapter began at the end of the nineteenth century, with the introduction of residency requirements for recent medical school graduates. Fresh medical school graduates needed to find a hospital in which to pursue their medical internships. Over the years, the residents played an increasingly important role in the staffs of hospitals, and hospitals began competing with each other for the best medical school graduates.
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- Game Theory , pp. 884 - 915Publisher: Cambridge University PressPrint publication year: 2013