The stable marriage problem: structure and algorithms
The stable marriage problem: structure and algorithms
Randomized algorithms
A fixed-point approach to stable matchings and some applications
Mathematics of Operations Research
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
Pure Nash equilibria in player-specific and weighted congestion games
Theoretical Computer Science
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
Market sharing games applied to content distribution in ad hoc networks
IEEE Journal on Selected Areas in Communications
Local matching dynamics in social networks
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Local matching dynamics in social networks
Information and Computation
Stable marriage and roommate problems with individual-based stability
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
Locally stable marriage with strict preferences
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
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Various economic interactions can be modeled as two-sided markets. A central solution concept for these markets is 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 they 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.