IDEAS home Printed from https://ideas.repec.org/p/unm/umagsb/2021004.html
   My bibliography  Save this paper

The computation of pairwise stable networks

Author

Listed:
  • Herings, P. Jean-Jacques

    (RS: GSBE Theme Data-Driven Decision-Making, RS: GSBE Theme Conflict & Cooperation, Microeconomics & Public Economics)

  • Zhan, Yang

Abstract

One of the most important stability concepts for network formation is pairwise stability. We develop a homotopy algorithm that is effective in computing pairwise stable networks for a generic network formation problem. To do so, we reformulate the concept of pairwise stability as a Nash equilibrium of a non-cooperative game played by the links in the network and adapt the linear tracing procedure for non-cooperative games to the network formation problem. As a by-product of our main result, we obtain that the number of pairwise stable networks is generically odd. We apply the algorithm to the connections model.

Suggested Citation

  • Herings, P. Jean-Jacques & Zhan, Yang, 2021. "The computation of pairwise stable networks," Research Memorandum 004, Maastricht University, Graduate School of Business and Economics (GSBE).
    • Handle: RePEc:unm:umagsb:2021004
    DOI: 10.26481/umagsb.2021004
    as

    Download full text from publisher

    File URL: https://cris.maastrichtuniversity.nl/ws/files/61693240/RM21004.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.26481/umagsb.2021004?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, December.
    2. Herings, P. Jean-Jacques & Peeters, Ronald J. A. P., 2004. "Stationary equilibria in stochastic games: structure, selection, and computation," Journal of Economic Theory, Elsevier, vol. 118(1), pages 32-60, September.
    3. Miyauchi, Yuhei, 2016. "Structural estimation of pairwise stable networks with nonnegative externality," Journal of Econometrics, Elsevier, vol. 195(2), pages 224-235.
    4. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702.
    5. Tim Hellmann, 2013. "On the existence and uniqueness of pairwise stable networks," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(1), pages 211-237, February.
    6. Govindan, Srihari & Wilson, Robert, 2009. "Global Newton Method for stochastic games," Journal of Economic Theory, Elsevier, vol. 144(1), pages 414-421, January.
    7. P. Herings & Ronald Peeters, 2010. "Homotopy methods to compute equilibria in game theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 119-156, January.
    8. Govindan, Srihari & Wilson, Robert, 2003. "A global Newton method to compute Nash equilibria," Journal of Economic Theory, Elsevier, vol. 110(1), pages 65-86, May.
    9. Andrew McLennan, 2005. "The Expected Number of Nash Equilibria of a Normal Form Game," Econometrica, Econometric Society, vol. 73(1), pages 141-174, January.
    10. Peixuan Li & Chuangyin Dang, 2020. "An Arbitrary Starting Tracing Procedure for Computing Subgame Perfect Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 667-687, August.
    11. P. Jean-Jacques Herings & Ronald J.A.P. Peeters, 2001. "symposium articles: A differentiable homotopy to compute Nash equilibria of n -person games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 18(1), pages 159-185.
    12. Eaves, B. Curtis & Schmedders, Karl, 1999. "General equilibrium models and homotopy methods," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1249-1279, September.
    13. Philippe Bich & Lisa Morhaim, 2020. "On the Existence of Pairwise Stable Weighted Networks," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1393-1404, November.
    14. Francis Bloch & Matthew Jackson, 2006. "Definitions of equilibrium in network formation games," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(3), pages 305-318, October.
    15. Michael P. Leung, 2020. "Equilibrium computation in discrete network games," Quantitative Economics, Econometric Society, vol. 11(4), pages 1325-1347, November.
    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. Philippe Bich & Julien Fixary, 2021. "Structure and oddness theorems for pairwise stable networks," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03287524, HAL.
    2. Philippe Bich & Julien Fixary, 2021. "Structure and oddness theorems for pairwise stable networks," Post-Print halshs-03287524, HAL.

    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. Chuangyin Dang & P. Jean-Jacques Herings & Peixuan Li, 2022. "An Interior-Point Differentiable Path-Following Method to Compute Stationary Equilibria in Stochastic Games," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1403-1418, May.
    2. P. Herings & Ronald Peeters, 2010. "Homotopy methods to compute equilibria in game theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 119-156, January.
    3. Cao, Yiyin & Dang, Chuangyin & Xiao, Zhongdong, 2022. "A differentiable path-following method to compute subgame perfect equilibria in stationary strategies in robust stochastic games and its applications," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1032-1050.
    4. Dang, Chuangyin & Herings, P. Jean-Jacques & Li, Peixuan, 2020. "An Interior-Point Path-Following Method to Compute Stationary Equilibria in Stochastic Games," Research Memorandum 001, Maastricht University, Graduate School of Business and Economics (GSBE).
    5. Li, Peixuan & Dang, Chuangyin & Herings, P.J.J., 2023. "Computing Perfect Stationary Equilibria in Stochastic Games," Other publications TiSEM 5b68f5d7-3209-4a1b-924c-6, Tilburg University, School of Economics and Management.
    6. Cao, Yiyin & Dang, Chuangyin, 2022. "A variant of Harsanyi's tracing procedures to select a perfect equilibrium in normal form games," Games and Economic Behavior, Elsevier, vol. 134(C), pages 127-150.
    7. P. Herings & Ronald Peeters, 2005. "A Globally Convergent Algorithm to Compute All Nash Equilibria for n-Person Games," Annals of Operations Research, Springer, vol. 137(1), pages 349-368, July.
    8. Yiyin Cao & Chuangyin Dang & Yabin Sun, 2022. "Complementarity Enhanced Nash’s Mappings and Differentiable Homotopy Methods to Select Perfect Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 192(2), pages 533-563, February.
    9. Dang, Chuangyin & Meng, Xiaoxuan & Talman, Dolf, 2015. "An Interior-Point Path-Following Method for Computing a Perfect Stationary Point of a Polynomial Mapping on a Polytope," Other publications TiSEM 07b7a0e7-f814-4ec2-a3a7-e, Tilburg University, School of Economics and Management.
    10. Bich, Philippe & Teteryatnikova, Mariya, 2023. "On perfect pairwise stable networks," Journal of Economic Theory, Elsevier, vol. 207(C).
    11. Herings, P. J. J. & Polemarchakis, H., 2002. "Equilibrium and arbitrage in incomplete asset markets with fixed prices," Journal of Mathematical Economics, Elsevier, vol. 37(2), pages 133-155, April.
    12. Herings, P.J.J., 2024. "Globally and Universally Convergent Price Adjustment Processes," Discussion Paper 2024-001, Tilburg University, Center for Economic Research.
    13. Bryan S. Graham, 2019. "Network Data," Papers 1912.06346, arXiv.org.
    14. Herings, P. Jean-Jacques & Peeters, Ronald J. A. P., 2004. "Stationary equilibria in stochastic games: structure, selection, and computation," Journal of Economic Theory, Elsevier, vol. 118(1), pages 32-60, September.
    15. Jean-Jacques Herings, P., 2002. "Universally converging adjustment processes--a unifying approach," Journal of Mathematical Economics, Elsevier, vol. 38(3), pages 341-370, November.
    16. Yang Zhan & Peixuan Li & Chuangyin Dang, 2020. "A differentiable path-following algorithm for computing perfect stationary points," Computational Optimization and Applications, Springer, vol. 76(2), pages 571-588, June.
    17. P. Jean-Jacques Herings & Ronald J. A. P. Peeters, 2003. "Equilibrium Selection In Stochastic Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 5(04), pages 307-326.
    18. Anne Balthasar, 2010. "Equilibrium tracing in strategic-form games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 39-54, January.
    19. Steffen Eibelshäuser & Victor Klockmann & David Poensgen & Alicia von Schenk, 2023. "The Logarithmic Stochastic Tracing Procedure: A Homotopy Method to Compute Stationary Equilibria of Stochastic Games," INFORMS Journal on Computing, INFORMS, vol. 35(6), pages 1511-1526, November.
    20. Philippe Bich & Lisa Morhaim, 2020. "On the Existence of Pairwise Stable Weighted Networks," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1393-1404, November.

    More about this item

    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:unm:umagsb:2021004. See general information about how to correct material in RePEc.

    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: Andrea Willems or Leonne Portz (email available below). General contact details of provider: https://edirc.repec.org/data/meteonl.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.