The stable marriage problem: structure and algorithms
The stable marriage problem: structure and algorithms
The average number of stable matchings
SIAM Journal on Discrete Mathematics
On likely solutions of a stable matching problem
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Algorithmic mechanism design (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
A BGP-based mechanism for lowest-cost routing
Proceedings of the twenty-first annual symposium on Principles of distributed computing
An approximate truthful mechanism for combinatorial auctions with single parameter agents
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Truthful Mechanisms for One-Parameter Agents
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
Cheating by men in the gale-shapley stable matching algorithm
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Anarchy, Stability, and Utopia: Creating Better Matchings
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
Cheating to get better roommates in a random stable matching
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Matching, cardinal utility, and social welfare
ACM SIGecom Exchanges
The college admissions problem with a continuum of students
Proceedings of the 12th ACM conference on Electronic commerce
Mechanism design in large games: incentives and privacy
Proceedings of the 5th conference on Innovations in theoretical computer science
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Many centralized two-sided markets form a matching between participants by running a stable marriage algorithm. It is a well-known fact that no matching mechanism based on a stable marriage algorithm can guarantee truthfulness as a dominant strategy for participants. However, as we will show in this paper, in a probabilistic setting where the preference lists of one side of the market are composed of only a constant (independent of the the size of the market) number of entries, each drawn from an arbitrary distribution, the number of participants that have more than one stable partner is vanishingly small. This proves (and generalizes) a conjecture of Roth and Peranson [23]. As a corollary of this result, we show that, with high probability, the truthful strategy is the best response for a given player when the other players are truthful. We also analyze equilibria of the deferred acceptance stable marriage game. We show that the game with complete information has an equilibrium in which a (1 - o(1)) fraction of the strategies are truthful in expectation. In the more realistic setting of a game of incomplete information, we will show that the set of truthful strategies form a (1 + o(1))-approximate Bayesian-Nash equilibrium. Our results have implications in many practical settings and were inspired by the work of Roth and Peranson [23] on the National Residency Matching Program.