Skip to main content
Springer Nature Link
Log in

Matching Dynamics with Constraints

  • Conference paper
Web and Internet Economics (WINE 2014)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 8877))

Included in the following conference series:

  • 1782 Accesses

Abstract

We study uncoordinated matching markets with additional local constraints that capture, e.g., restricted information, visibility, or externalities in markets. Each agent is a node in a fixed matching network and strives to be matched to another agent. Each agent has a complete preference list over all other agents it can be matched with. However, depending on the constraints and the current state of the game, not all possible partners are available for matching at all times.

For correlated preferences, we propose and study a general class of hedonic coalition formation games that we call coalition formation games with constraints. This class includes and extends many recently studied variants of stable matching, such as locally stable matching, socially stable matching, or friendship matching. Perhaps surprisingly, we show that all these variants are encompassed in a class of “consistent” instances that always allow a polynomial improvement sequence to a stable state. In addition, we show that for consistent instances there always exists a polynomial sequence to every reachable state. Our characterization is tight in the sense that we provide exponential lower bounds when each of the requirements for consistency is violated.

We also analyze matching with uncorrelated preferences, where we obtain a larger variety of results. While socially stable matching always allows a polynomial sequence to a stable state, for other classes different additional assumptions are sufficient to guarantee the same results. For the problem of reaching a given stable state, we show NP-hardness in almost all considered classes of matching games.

Supported by DFG Cluster of Excellence MMCI and grant Ho 3831/3-1.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Abraham, D., Levavi, A., Manlove, D., O’Malley, G.: The stable roommates problem with globally ranked pairs. Internet Math. 5(4), 493–515 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  2. Ackermann, H., Goldberg, P., Mirrokni, V., Röglin, H., Vöcking, B.: Uncoordinated two-sided matching markets. SIAM J. Comput. 40(1), 92–106 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  3. Anshelevich, E., Bhardwaj, O., Hoefer, M.: Friendship and stable matching. In: Bodlaender, H.L., Italiano, G.F. (eds.) ESA 2013. LNCS, vol. 8125, pp. 49–60. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  4. Arcaute, E., Vassilvitskii, S.: Social networks and stable matchings in the job market. In: Leonardi, S. (ed.) WINE 2009. LNCS, vol. 5929, pp. 220–231. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  5. Askalidis, G., Immorlica, N., Kwanashie, A., Manlove, D.F., Pountourakis, E.: Socially stable matchings in the hospitals/Residents problem. In: Dehne, F., Solis-Oba, R., Sack, J.-R. (eds.) WADS 2013. LNCS, vol. 8037, pp. 85–96. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  6. Biró, P., Bomhoff, M., Golovach, P.A., Kern, W., Paulusma, D.: Solutions for the stable roommates problem with payments. Theoret. Comput. Sci. 540, 53–61 (2014)

    Article  MathSciNet  Google Scholar 

  7. Biró, P., Cechlárová, K., Fleiner, T.: The dynamics of stable matchings and half-matchings for the stable marriage and roommates problems. Int. J. Game Theory 36(3-4), 333–352 (2008)

    Article  MATH  Google Scholar 

  8. Biró, P., Norman, G.: Analysis of stochastic matching markets. Int. J. Game Theory 42(4), 1021–1040 (2013)

    Article  MATH  Google Scholar 

  9. Blum, Y., Roth, A., Rothblum, U.: Vacancy chains and equilibration in senior-level labor markets. J. Econom. Theory 76, 362–411 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  10. Blum, Y., Rothblum, U.: “Timing is everything” and martial bliss. J. Econom. Theory 103, 429–442 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  11. Bogomolnaia, A., Jackson, M.: The stability of hedonic coalition structures. Games Econom. Behav. 38, 201–230 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  12. Cechlárova, K.: Stable partition problem. In: Encyclopedia of Algorithms (2008)

    Google Scholar 

  13. Diamantoudi, E., Miyagawa, E., Xue, L.: Random paths to stability in the roommates problem. Games Econom. Behav. 48(1), 18–28 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  14. Hajduková, J.: Coalition formation games: A survey. Intl. Game Theory Rev. 8(4), 613–641 (2006)

    Article  MATH  Google Scholar 

  15. Hoefer, M.: Local matching dynamics in social networks. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part II. LNCS, vol. 6756, pp. 113–124. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  16. Hoefer, M.: Local matching dynamics in social networks. Inf. Comput. 222, 20–35 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  17. Hoefer, M., Penn, M., Polukarov, M., Skopalik, A., Vöcking, B.: Considerate equilibrium. In: Proc. 22nd Intl. Joint Conf. Artif. Intell. (IJCAI), pp. 234–239 (2011)

    Google Scholar 

  18. Hoefer, M., Wagner, L.: Designing profit shares in matching and coalition formation games. In: Chen, Y., Immorlica, N. (eds.) WINE 2013. LNCS, vol. 8289, pp. 249–262. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  19. Hoefer, M., Wagner, L.: Locally stable marriage with strict preferences. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds.) ICALP 2013, Part II. LNCS, vol. 7966, pp. 620–631. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  20. Hoffman, M., Moeller, D., Paturi, R.: Jealousy graphs: Structure and complexity of decentralized stable matching. In: Chen, Y., Immorlica, N. (eds.) WINE 2013. LNCS, vol. 8289, pp. 263–276. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  21. Inarra, E., Larrea, C., Moris, E.: Random paths to P-stability in the roommates problem. Int. J. Game Theory 36(3-4), 461–471 (2008)

    Article  MATH  Google Scholar 

  22. Inarra, E., Larrea, C., Moris, E.: The stability of the roommate problem revisited. Core Discussion Paper 2010/7 (2010)

    Google Scholar 

  23. Irving, R.: An efficient algorithm for the “stable roommates” problem. J. Algorithms 6(4), 577–595 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  24. Klaus, B., Klijn, F., Walzl, M.: Stochastic stability for roommate markets. J. Econom. Theory 145, 2218–2240 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  25. Knuth, D.: Marriages stables et leurs relations avec d’autres problemes combinatoires. Les Presses de l’Université de Montréal (1976)

    Google Scholar 

  26. Manlove, D.: Algorithmics of Matching Under Preferences. World Scientific (2013)

    Google Scholar 

  27. Mathieu, F.: Acyclic preference-based systems. In: Shen, X., Yu, H., Buford, J., Akon, M. (eds.) Handbook of Peer-to-Peer Networking. Springer (2010)

    Google Scholar 

  28. Roth, A., Vate, J.V.: Random paths to stability in two-sided matching. Econometrica 58(6), 1475–1480 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  29. Woeginger, G.J.: Core stability in hedonic coalition formation. In: van Emde Boas, P., Groen, F.C.A., Italiano, G.F., Nawrocki, J., Sack, H. (eds.) SOFSEM 2013. LNCS, vol. 7741, pp. 33–50. Springer, Heidelberg (2013)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Max-Planck-Institut für Informatik and Saarland University, Germany

    Martin Hoefer

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

    Lisa Wagner

Authors
  1. Martin Hoefer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lisa Wagner
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Microsoft Research, Haidian District, 100080, Beijing, China

    Tie-Yan Liu

  2. The Hong Kong University of Science and Technology, Kowloon, Hong Kong

    Qi Qi

  3. Deptartment of Management Science and Engineering, Stanford University, 94305-4121, Stanford, CA, USA

    Yinyu Ye

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Hoefer, M., Wagner, L. (2014). Matching Dynamics with Constraints. In: Liu, TY., Qi, Q., Ye, Y. (eds) Web and Internet Economics. WINE 2014. Lecture Notes in Computer Science, vol 8877. Springer, Cham. https://doi.org/10.1007/978-3-319-13129-0_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-13129-0_12

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13128-3

  • Online ISBN: 978-3-319-13129-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics