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An allocation rule for dynamic random network formation processes

  • Jean-François Caulier

    ()

    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne)

  • Michel Grabisch

    ()

    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris)

  • Agnieszka Rusinowska

    ()

    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris)

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.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00881125.

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Date of creation: Aug 2013
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Handle: RePEc:hal:cesptp:halshs-00881125
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  1. David Pérez-Castrillo & David Wettstein, 2004. "Forming Efficient Networks," Working Papers 123, Barcelona Graduate School of Economics.
  2. Vincent Vannetelbosch & Jean-François Caulier & Ana Mauleon, 2009. "Contractually Stable Networks," Working Papers 2009.47, Fondazione Eni Enrico Mattei.
  3. Dutta, Bhaskar & Ghosal, Sayantan & Ray, Debraj, 2005. "Farsighted network formation," Journal of Economic Theory, Elsevier, vol. 122(2), pages 143-164, June.
  4. Page Jr., Frank H. & Wooders, Myrna, 2007. "Networks and clubs," Journal of Economic Behavior & Organization, Elsevier, vol. 64(3-4), pages 406-425.
  5. Frank H. Page, Jr. & Myrna H. Wooders, 2006. "Strategic Basins of Attraction, the Path Dominance Core, and Network Formation Games," Vanderbilt University Department of Economics Working Papers 0614, Vanderbilt University Department of Economics.
  6. HERINGS, Jean-Jacques & MAULEON, Ana & VANNETELBOSCH, Vincent, . "Farsightedly stable networks," CORE Discussion Papers RP -2171, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. 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.
  8. Page Jr, Frank H & Wooders, Myrna H & Kamat, Samir, 2001. "Networks And Farsighted Stability," The Warwick Economics Research Paper Series (TWERPS) 621, University of Warwick, Department of Economics.
  9. Guillaume Haeringer, 1998. "A new weight scheme for the Shapley value," Game Theory and Information 9807001, EconWPA.
  10. Konishi, Hideo & Ray, Debraj, 2003. "Coalition formation as a dynamic process," Journal of Economic Theory, Elsevier, vol. 110(1), pages 1-41, May.
  11. Hamiache, Gerard, 1999. "A Value with Incomplete Communication," Games and Economic Behavior, Elsevier, vol. 26(1), pages 59-78, January.
  12. Ghintran, Amandine, 2013. "Weighted position values," Mathematical Social Sciences, Elsevier, vol. 65(3), pages 157-163.
  13. Watts, Alison, 2002. "Non-myopic formation of circle networks," Economics Letters, Elsevier, vol. 74(2), pages 277-282, January.
  14. 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.
  15. Watts, Alison, 2001. "A Dynamic Model of Network Formation," Games and Economic Behavior, Elsevier, vol. 34(2), pages 331-341, February.
  16. 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.
  17. Jackson, Matthew O., 1998. "The Evolution of Social and Economic Networks," Working Papers 1044, California Institute of Technology, Division of the Humanities and Social Sciences.
  18. Slikker, Marco, 2007. "Bidding for surplus in network allocation problems," Journal of Economic Theory, Elsevier, vol. 137(1), pages 493-511, November.
  19. repec:hal:journl:halshs-00749950 is not listed on IDEAS
  20. repec:hal:cesptp:halshs-00749950 is not listed on IDEAS
  21. 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.
  22. Ulrich Faigle & Michel Grabisch, 2012. "Values for Markovian coalition processes," Economic Theory, Springer, vol. 51(3), pages 505-538, November.
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