Local Matching Dynamics in Social Networks
We study stable marriage and roommates problems in graphs with locality constraints. Each player is a node in a social network and has an incentive to match with other players. The value of a match is specified by an edge weight. Players explore possible matches only based on their current neighborhood. We study convergence of natural better-response dynamics that converge to locally stable matchings – matchings that allow no incentive to deviate with respect to their imposed information structure in the social network. For every starting state we construct in polynomial time a sequence of polynomially many better-response moves to a locally stable matching. However, for a large class of oblivious dynamics including random and concurrent better-response the convergence time turns out to be exponential. In contrast, convergence time becomes polynomial if we allow the players to have a small amount of random memory, even for many-to-many matchings and more general notions of neighborhood.
KeywordsStable Match Preference List Social Link Matching Edge Marked Vertex
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- 4.Anshelevich, E., Hoefer, M.: Contribution games in social networks. In: Proc. 18th European Symposium on Algorithms (ESA), vol. 1, pp. 158–169 (2010)Google Scholar
- 6.Echenique, F., Oviedo, J.: A theory of stability in many-to-many matching markets. Theoretical Economics 1(2), 233–273 (2006)Google Scholar
- 17.Knuth, D.: Marriages Stables et leurs relations avec d’autres problemes combinatoires. Les Presses de l’Université de Montréal (1976)Google Scholar