IDEAS home Printed from https://ideas.repec.org/p/mse/cesdoc/13063.html
   My bibliography  Save this paper

An allocation rule for dynamic random network formation processes

Author

Abstract

Most allocation rules for network games presented in the literature assume that the network structure is fixed. We put explicit emphasis on the construction of networks and examine the dynamic formation of networks whose evolution across time periods is stochastic. Time-series of networks are studied that describe processes of network formation where links may appear or disappear at any period. Moreover, convergence to an efficient network is not necessarily prescribed. Transitions from one network to another are random and yield a Markov chain. We propose the link-based allocation rule for such dynamic random network formation processes and provide its axiomatic characterization. By considering a monotone game and a particular (natural) network formation process we recover the link-based flexible network allocation rule of Jackson

Suggested Citation

  • Jean-François Caulier & Michel Grabisch & Agnieszka Rusinowska, 2013. "An allocation rule for dynamic random network formation processes," Documents de travail du Centre d'Economie de la Sorbonne 13063, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  • Handle: RePEc:mse:cesdoc:13063
    as

    Download full text from publisher

    File URL: ftp://mse.univ-paris1.fr/pub/mse/CES2013/13063.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Laurence Kranich & Andrés Perea & Hans Peters, 2005. "Core Concepts For Dynamic Tu Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 43-61.
    2. Jean-François Caulier & Ana Mauleon & Vincent Vannetelbosch, 2013. "Contractually stable networks," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 483-499, May.
    3. Page, Frank Jr. & Wooders, Myrna H. & Kamat, Samir, 2005. "Networks and farsighted stability," Journal of Economic Theory, Elsevier, vol. 120(2), pages 257-269, February.
    4. Dutta, Bhaskar & Ghosal, Sayantan & Ray, Debraj, 2005. "Farsighted network formation," Journal of Economic Theory, Elsevier, vol. 122(2), pages 143-164, June.
    5. Page Jr., Frank H. & Wooders, Myrna, 2009. "Strategic basins of attraction, the path dominance core, and network formation games," Games and Economic Behavior, Elsevier, vol. 66(1), pages 462-487, May.
    6. Konishi, Hideo & Ray, Debraj, 2003. "Coalition formation as a dynamic process," Journal of Economic Theory, Elsevier, vol. 110(1), pages 1-41, May.
    7. Hamiache, Gerard, 1999. "A Value with Incomplete Communication," Games and Economic Behavior, Elsevier, vol. 26(1), pages 59-78, January.
    8. Stef Tijs & Anne van den Nouweland & Bhaskar Dutta, 1998. "Link formation in cooperative situations," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(2), pages 245-256.
    9. Haeringer, Guillaume, 2006. "A new weight scheme for the Shapley value," Mathematical Social Sciences, Elsevier, vol. 52(1), pages 88-98, July.
    10. van den Nouweland, Anne & Borm, Peter & Tijs, Stef, 1992. "Allocation Rules for Hypergraph Communication Situations," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(3), pages 255-268.
    11. Helga Habis & P. Herings, 2013. "Stochastic bankruptcy games," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(4), pages 973-988, November.
    12. Noemí Navarro, 2014. "Expected fair allocation in farsighted network formation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(2), pages 287-308, August.
    13. Ghintran, Amandine, 2013. "Weighted position values," Mathematical Social Sciences, Elsevier, vol. 65(3), pages 157-163.
    14. Borm, P.E.M. & Owen, G. & Tijs, S.H., 1992. "On the position value for communication situations," Other publications TiSEM 5a8473e4-1df7-42df-ad53-f, Tilburg University, School of Economics and Management.
    15. Jackson, Matthew O. & Wolinsky, Asher, 1996. "A Strategic Model of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 71(1), pages 44-74, October.
    16. Page Jr., Frank H. & Wooders, Myrna, 2007. "Networks and clubs," Journal of Economic Behavior & Organization, Elsevier, vol. 64(3-4), pages 406-425.
    17. A. Ghintran & E. González-Arangüena & C. Manuel, 2012. "A probabilistic position value," Annals of Operations Research, Springer, vol. 201(1), pages 183-196, December.
    18. Herings, P. Jean-Jacques & Mauleon, Ana & Vannetelbosch, Vincent, 2009. "Farsightedly stable networks," Games and Economic Behavior, Elsevier, vol. 67(2), pages 526-541, November.
    19. Matthew O. Jackson & Bhaskar Dutta, 2000. "original papers : The stability and efficiency of directed communication networks," Review of Economic Design, Springer;Society for Economic Design, vol. 5(3), pages 251-272.
    20. Predtetchinski, Arkadi & Herings, P. Jean-Jacques & Peters, Hans, 2002. "The strong sequential core for two-period economies," Journal of Mathematical Economics, Elsevier, vol. 38(4), pages 465-482, December.
    21. Predtetchinski, Arkadi, 2007. "The strong sequential core for stationary cooperative games," Games and Economic Behavior, Elsevier, vol. 61(1), pages 50-66, October.
    22. Bilbao, J.M. & Jimenez, N. & Lopez, J.J., 2006. "A note on a value with incomplete communication," Games and Economic Behavior, Elsevier, vol. 54(2), pages 419-429, February.
    23. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    24. Perez-Castrillo, David & Wettstein, David, 2005. "Forming efficient networks," Economics Letters, Elsevier, vol. 87(1), pages 83-87, April.
    25. Ehud Lehrer & Marco Scarsini, 2013. "On the Core of Dynamic Cooperative Games," Dynamic Games and Applications, Springer, vol. 3(3), pages 359-373, September.
    26. Ulrich Faigle & Michel Grabisch, 2013. "A note on values for Markovian coalition processes," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(2), pages 111-122, November.
    27. Habis, Helga & Herings, P. Jean-Jacques, 2011. "Transferable utility games with uncertainty," Journal of Economic Theory, Elsevier, vol. 146(5), pages 2126-2139, September.
    28. Guillaume Haeringer, 1999. "Weighted Myerson Value," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 1(02), pages 187-192.
    29. Perez-Castrillo, David & Wettstein, David, 2001. "Bidding for the Surplus : A Non-cooperative Approach to the Shapley Value," Journal of Economic Theory, Elsevier, vol. 100(2), pages 274-294, October.
    30. Ulrich Faigle & Michel Grabisch, 2012. "Values for Markovian coalition processes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(3), pages 505-538, November.
    31. Slikker, Marco, 2007. "Bidding for surplus in network allocation problems," Journal of Economic Theory, Elsevier, vol. 137(1), pages 493-511, November.
    32. Oviedo, Jorge, 2000. "The core of a repeated n-person cooperative game," European Journal of Operational Research, Elsevier, vol. 127(3), pages 519-524, December.
    33. Watts, Alison, 2002. "Non-myopic formation of circle networks," Economics Letters, Elsevier, vol. 74(2), pages 277-282, January.
    34. Helga Habis & P. Jean-Jacques Herings, 2010. "A Note On The Weak Sequential Core Of Dynamic Tu Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 12(04), pages 407-416.
    35. Dutta, Bhaskar & Mutuswami, Suresh, 1997. "Stable Networks," Journal of Economic Theory, Elsevier, vol. 76(2), pages 322-344, October.
      • Dutta, Bhaskar & Mutuswami, Suresh, 1996. "Stable Networks," Working Papers 971, California Institute of Technology, Division of the Humanities and Social Sciences.
    36. Jackson, Matthew O. & Watts, Alison, 2002. "The Evolution of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 106(2), pages 265-295, October.
    37. Hans Haller & Jurjen Kamphorst & Sudipta Sarangi, 2007. "(Non-)existence and Scope of Nash Networks," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(3), pages 597-604, June.
    38. Rodrigo Harrison & Roberto Muñoz, 2008. "Stability and equilibrium selection in a link formation game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 37(2), pages 335-345, November.
    39. Watts, Alison, 2001. "A Dynamic Model of Network Formation," Games and Economic Behavior, Elsevier, vol. 34(2), pages 331-341, February.
    40. Jean-François Caulier & Ana Mauleon & Vincent Vannetelbosch, 2013. "Contractually stable networks," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 483-499, May.
    41. van den Nouweland, Anne & Slikker, Marco, 2012. "An axiomatic characterization of the position value for network situations," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 266-271.
    42. Page Jr., Frank H. & Wooders, Myrna, 2010. "Club networks with multiple memberships and noncooperative stability," Games and Economic Behavior, Elsevier, vol. 70(1), pages 12-20, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. María Gómez-Rúa & Juan Vidal-Puga, 2017. "A monotonic and merge-proof rule in minimum cost spanning tree situations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(3), pages 813-826, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Joost Vandenbossche & Thomas Demuynck, 2013. "Network Formation with Heterogeneous Agents and Absolute Friction," Computational Economics, Springer;Society for Computational Economics, vol. 42(1), pages 23-45, June.
    2. Youngsub Chun & Sunghoon Hong & Bong Chan Koh, 2017. "Population invariance properties of social and economic networks," International Journal of Economic Theory, The International Society for Economic Theory, vol. 13(3), pages 255-267, September.
    3. Dutta, Bhaskar & Ghosal, Sayantan & Ray, Debraj, 2005. "Farsighted network formation," Journal of Economic Theory, Elsevier, vol. 122(2), pages 143-164, June.
    4. Frank H. Page & Myrna H. Wooders, 2009. "Endogenous Network Dynamics," Working Papers 2009.28, Fondazione Eni Enrico Mattei.
    5. Kirchsteiger, Georg & Mantovani, Marco & Mauleon, Ana & Vannetelbosch, Vincent, 2016. "Limited farsightedness in network formation," Journal of Economic Behavior & Organization, Elsevier, vol. 128(C), pages 97-120.
    6. Chenghong Luo & Ana Mauleon & Vincent Vannetelbosch, 2021. "Network formation with myopic and farsighted players," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(4), pages 1283-1317, June.
    7. Chenghong Luo & Ana Mauleon & Vincent Vannetelbosch, 0. "Network formation with myopic and farsighted players," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 0, pages 1-35.
    8. Page, Frank Jr. & Wooders, Myrna H. & Kamat, Samir, 2005. "Networks and farsighted stability," Journal of Economic Theory, Elsevier, vol. 120(2), pages 257-269, February.
    9. Marco Mantovani & Georg Kirchsteiger & Ana Mauleon & Vincent Vannetelbosch, 2011. "Myopic or Farsighted? An Experiment on Network Formation," Working Papers 2011.45, Fondazione Eni Enrico Mattei.
    10. Carayol, Nicolas & Delille, Rémy & Vannetelbosch, Vincent, 2015. "Allocating value among farsighted players in network formation," Economics Letters, Elsevier, vol. 137(C), pages 50-53.
    11. Mauleon, Ana & Sempere-Monerris, Jose J. & Vannetelbosch, Vincent, 2021. "Limited Farsightedness in R&D Network Formation," LIDAM Discussion Papers CORE 2021006, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. HERINGS, P. Jean-Jacques & MAULEON, Ana & VANNETELBOSCH, Vincent, 2014. "Stability of networks under level-K farsightedness," LIDAM Discussion Papers CORE 2014032, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. Roland Pongou & Roberto Serrano, 2009. "A dynamic theory of fidelity networks with an application to the spread of HIV/AIDS," Working Papers 2009-03, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
    14. Herings, P. Jean-Jacques & Mauleon, Ana & Vannetelbosch, Vincent, 2009. "Farsightedly stable networks," Games and Economic Behavior, Elsevier, vol. 67(2), pages 526-541, November.
    15. Jackson, Matthew O. & van den Nouweland, Anne, 2005. "Strongly stable networks," Games and Economic Behavior, Elsevier, vol. 51(2), pages 420-444, May.
    16. Mauleon, Ana & Roehl, Nils & Vannetelbosch, Vincent, 2018. "Constitutions and groups," Games and Economic Behavior, Elsevier, vol. 107(C), pages 135-152.
    17. Page Jr., Frank H. & Wooders, Myrna, 2009. "Strategic basins of attraction, the path dominance core, and network formation games," Games and Economic Behavior, Elsevier, vol. 66(1), pages 462-487, May.
    18. Boncinelli, Leonardo & Pin, Paolo, 2014. "Efficiency and Stability in a Process of Teams Formation," MPRA Paper 56356, University Library of Munich, Germany.
    19. Pongou, Roland & Serrano, Roberto, 2016. "Volume of trade and dynamic network formation in two-sided economies," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 147-163.
    20. Matthew O. Jackson, 2003. "A Survey of Models of Network Formation: Stability and Efficiency," Game Theory and Information 0303011, University Library of Munich, Germany.

    More about this item

    Keywords

    Dynamic networks; network game; link-based allocation rule; Markov chain; characterization;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:mse:cesdoc:13063. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/cenp1fr.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Lucie Label (email available below). General contact details of provider: https://edirc.repec.org/data/cenp1fr.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.