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Local Matching Dynamics in Social Networks

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Automata, Languages and Programming (ICALP 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6756))

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Abstract

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.

Supported by DFG grant Ho 3831/3-1.

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Author information

Authors and Affiliations

  1. Dept. of Computer Science, RWTH Aachen University, Germany

    Martin Hoefer

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  1. Martin Hoefer
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Editors and Affiliations

  1. ICE-TCS, School of Computer Science, Reykjavik University, Menntavegur 1, IS 101, Reykjavik, Iceland

    Luca Aceto

  2. Fakultät für Informatik, Universität Wien, Universitätsstraße10/9, 1090, Wien, Österreich, Austria

    Monika Henzinger

  3. Department of Applied Mathematics, Charles University, Malostranské nám. 25, 118 00, Praha 1, Czech Republic

    Jiří Sgall

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© 2011 Springer-Verlag Berlin Heidelberg

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Hoefer, M. (2011). Local Matching Dynamics in Social Networks. In: Aceto, L., Henzinger, M., Sgall, J. (eds) Automata, Languages and Programming. ICALP 2011. Lecture Notes in Computer Science, vol 6756. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22012-8_8

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  • DOI: https://doi.org/10.1007/978-3-642-22012-8_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22011-1

  • Online ISBN: 978-3-642-22012-8

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