The stable marriage problem: structure and algorithms
The stable marriage problem: structure and algorithms
A fixed-point approach to stable matchings and some applications
Mathematics of Operations Research
Market sharing games applied to content distribution in ad-hoc networks
Proceedings of the 5th ACM international symposium on Mobile ad hoc networking and computing
Tight approximation algorithms for maximum general assignment problems
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Approximation algorithms for distributed and selfish agents
Approximation algorithms for distributed and selfish agents
A unified approach to congestion games and two-sided markets
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
The stable roommates problem with globally-ranked pairs
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Upper bounds for stabilization in acyclic preference-based systems
SSS'07 Proceedings of the 9h international conference on Stabilization, safety, and security of distributed systems
Pure nash equilibria in player-specific and weighted congestion games
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
Uncoordinated two-sided matching markets
ACM SIGecom Exchanges
Anarchy, Stability, and Utopia: Creating Better Matchings
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
Designing a Two-Sided Matching Protocol under Asymmetric Information
PRIMA '09 Proceedings of the 12th International Conference on Principles of Practice in Multi-Agent Systems
Contribution games in social networks
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Local dynamics in bargaining networks via random-turn games
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Matching, cardinal utility, and social welfare
ACM SIGecom Exchanges
Distributed algorithms via gradient descent for fisher markets
Proceedings of the 12th ACM conference on Electronic commerce
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Various economic interactions can be modeled as two-sided markets. A central solution concept to these markets are stable matchings, introduced by Gale and Shapley. It is well known that stable matchings can be computed in polynomial time, but many real-life markets lack a central authority to match agents. In those markets, matchings are formed by actions of self-interested agents. Knuth introduced uncoordinated two-sided markets and showed that the uncoordinated better response dynamics may cycle. However, Roth and Vande Vate showed that the random better response dynamics converges to a stable matching with probability one, but did not address the question of convergence time. In this paper, we give an exponential lower bound for the convergence time of the random better response dynamics in two-sided markets. We also extend the results for the better response dynamics to the best response dynamics, i.e., we present a cycle of best responses, and prove that the random best response dynamics converges to a stable matching with probability one, but its convergence time is exponential. Additionally, we identify the special class of correlated matroid two-sided markets with real-life applications for which we prove that the random best response dynamics converges in expected polynomial time.