IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v237y2014i2p566-579.html
   My bibliography  Save this article

Asymmetric flow networks

Author

Listed:
  • Olaizola, Norma
  • Valenciano, Federico

Abstract

This paper provides a new model of network formation that bridges the gap between the two benchmark game-theoretic models by Bala and Goyal (2000a) – the one-way flow model, and the two-way flow model – and includes both as limiting cases. As in both the said models, a link can be initiated unilaterally by any player with any other in what we call an “asymmetric flow” network, and the flow through a link towards the player who supports it is perfect. Unlike those models, there is friction or decay in the opposite direction. When this decay is complete there is no flow and this corresponds to the one-way flow model. The limit case when the decay in the opposite direction (and asymmetry) disappears corresponds to the two-way flow model. We characterize stable and strictly stable architectures for the whole range of parameters of this “intermediate” and more general model. A study of the efficiency of these architectures shows that in general stability and efficiency do not go together. We also prove the convergence of Bala and Goyal’s dynamic model in this context.

Suggested Citation

  • Olaizola, Norma & Valenciano, Federico, 2014. "Asymmetric flow networks," European Journal of Operational Research, Elsevier, vol. 237(2), pages 566-579.
    • Handle: RePEc:eee:ejores:v:237:y:2014:i:2:p:566-579
    DOI: 10.1016/j.ejor.2014.01.048
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221714000691
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2014.01.048?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Hellmann, Tim & Staudigl, Mathias, 2014. "Evolution of social networks," European Journal of Operational Research, Elsevier, vol. 234(3), pages 583-596.
    2. Sanjeev Goyal, 2007. "Introduction to Connections: An Introduction to the Economics of Networks," Introductory Chapters, in: Connections: An Introduction to the Economics of Networks, Princeton University Press.
    3. Jean Derks & Martijn Tennekes, 2009. "A note on the existence of Nash networks in one-way flow models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 41(3), pages 515-522, December.
    4. Pascal Billand & Christophe Bravard & Sudipta Sarangi, 2008. "Existence of Nash networks in one-way flow models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 37(3), pages 491-507, December.
    5. Feri, Francesco, 2007. "Stochastic stability in networks with decay," Journal of Economic Theory, Elsevier, vol. 135(1), pages 442-457, July.
    6. Janssen, R.H.P. & Monsuur, H., 2012. "Stable network topologies using the notion of covering," European Journal of Operational Research, Elsevier, vol. 218(3), pages 755-763.
    7. 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.
    8. Skorin-Kapov, Nina & Furdek, Marija & Aparicio Pardo, Ramon & Mariño, Pablo Pavón, 2012. "Wavelength assignment for reducing in-band crosstalk attack propagation in optical networks: ILP formulations and heuristic algorithms," European Journal of Operational Research, Elsevier, vol. 222(3), pages 418-429.
    9. Bloch, Francis & Dutta, Bhaskar, 2009. "Communication networks with endogenous link strength," Games and Economic Behavior, Elsevier, vol. 66(1), pages 39-56, May.
    10. Hojman, Daniel A. & Szeidl, Adam, 2008. "Core and periphery in networks," Journal of Economic Theory, Elsevier, vol. 139(1), pages 295-309, March.
    11. Venkatesh Bala & Sanjeev Goyal, 2000. "original papers : A strategic analysis of network reliability," Review of Economic Design, Springer;Society for Economic Design, vol. 5(3), pages 205-228.
    12. Harmsen - van Hout, Marjolein J.W. & Herings, P. Jean-Jacques & Dellaert, Benedict G.C., 2013. "Communication network formation with link specificity and value transferability," European Journal of Operational Research, Elsevier, vol. 229(1), pages 199-211.
    13. Goyal, Sanjeev & Vega-Redondo, Fernando, 2005. "Network formation and social coordination," Games and Economic Behavior, Elsevier, vol. 50(2), pages 178-207, February.
    14. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
    15. Olaizola, Norma & Valenciano, Federico, 2013. "Network formation under linking constraints," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 5194-5205.
    16. Andrea Galeotti, 2006. "One-way flow networks: the role of heterogeneity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(1), pages 163-179, September.
    17. Galeotti, Andrea & Goyal, Sanjeev & Kamphorst, Jurjen, 2006. "Network formation with heterogeneous players," Games and Economic Behavior, Elsevier, vol. 54(2), pages 353-372, February.
    18. A. B. Dieker & J. Shin, 2013. "From Local to Global Stability in Stochastic Processing Networks Through Quadratic Lyapunov Functions," Mathematics of Operations Research, INFORMS, vol. 38(4), pages 638-664, November.
    19. Norma Olaizola & Federico Valenciano, 2014. "One-way flow network formation under constraints," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 624-643, July.
    20. McBride, Michael, 2006. "Imperfect monitoring in communication networks," Journal of Economic Theory, Elsevier, vol. 126(1), pages 97-119, January.
    21. Monsuur, Herman, 2007. "Stable and emergent network topologies: A structural approach," European Journal of Operational Research, Elsevier, vol. 183(1), pages 432-441, November.
    22. Daron Acemoğlu & Giacomo Como & Fabio Fagnani & Asuman Ozdaglar, 2013. "Opinion Fluctuations and Disagreement in Social Networks," Mathematics of Operations Research, INFORMS, vol. 38(1), pages 1-27, February.
    23. Lim, Gino J. & Zangeneh, Shabnam & Reza Baharnemati, M. & Assavapokee, Tiravat, 2012. "A capacitated network flow optimization approach for short notice evacuation planning," European Journal of Operational Research, Elsevier, vol. 223(1), pages 234-245.
    24. 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.
    25. Christophe Bravard & Sudipta Sarangi & Pascal Billand, 2008. "A Note on Existence of Nash Networks in One-way Flow," Economics Bulletin, AccessEcon, vol. 3(79), pages 1-4.
    26. repec:ebl:ecbull:v:3:y:2008:i:79:p:1-4 is not listed on IDEAS
    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. Rêgo, Leandro Chaves & dos Santos, Andrea Maria, 2019. "Co-authorship model with link strength," European Journal of Operational Research, Elsevier, vol. 272(2), pages 587-594.
    2. Ashrafi, M. & Khanjani, M.J. & Fadaei-Kermani, E. & Barani, G.A., 2015. "Farm drainage channel network optimization by improved modified minimal spanning tree," Agricultural Water Management, Elsevier, vol. 161(C), pages 1-8.
    3. Harmsen - van Hout, Marjolein J.W. & Dellaert, Benedict G.C. & Herings, P. Jean-Jacques, 2016. "Heuristic decision making in network linking," European Journal of Operational Research, Elsevier, vol. 251(1), pages 158-170.
    4. repec:ehu:ikerla:13425 is not listed on IDEAS
    5. repec:ehu:ikerla:13991 is not listed on IDEAS
    6. Agustín G. Bonifacio & Elena Inarra & Pablo Neme, 2022. "Stable Decompositions of Coalition Formation Games," Working Papers 110, Red Nacional de Investigadores en Economía (RedNIE).
    7. Choi, S. & Goyal, S. & Guo, F. & Moisan, F., 2024. "Experimental Evidence on Group Size Effects in Network Formation Games," Janeway Institute Working Papers 2412, Faculty of Economics, University of Cambridge.
    8. Olaizola, Norma & Valenciano, Federico, 2015. "Unilateral vs. bilateral link-formation: A transition without decay," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 13-28.
    9. Norma Olaizola & Federico Valenciano, 2018. "A unifying model of strategic network formation," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(4), pages 1033-1063, November.
    10. repec:ehu:ikerla:14746 is not listed on IDEAS
    11. Bonifacio, A.G. & Inarra, E. & Neme, P., 2024. "A characterization of absorbing sets in coalition formation games," Games and Economic Behavior, Elsevier, vol. 148(C), pages 1-22.
    12. Tenev, Anastas P., 2024. "“Friends Are Thieves of Time”: Heuristic attention sharing in stable friendship networks," Journal of Economic Behavior & Organization, Elsevier, vol. 224(C), pages 785-809.
    13. Norma Olaizola & Federico Valenciano, 2016. "From bilateral two-way to unilateral one-way flow link-formation," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 7(2), pages 257-278, June.
    14. Ping Sun & Elena Parilina, 2024. "Dynamic Network Formation with Ordered Partitioning and Incomplete Information," Dynamic Games and Applications, Springer, vol. 14(4), pages 921-958, September.

    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. repec:ehu:ikerla:8633 is not listed on IDEAS
    2. repec:ehu:ikerla:6257 is not listed on IDEAS
    3. Billand, Pascal & Bravard, Christophe & Sarangi, Sudipta, 2012. "Existence of Nash networks and partner heterogeneity," Mathematical Social Sciences, Elsevier, vol. 64(2), pages 152-158.
    4. Hellmann, Tim & Staudigl, Mathias, 2014. "Evolution of social networks," European Journal of Operational Research, Elsevier, vol. 234(3), pages 583-596.
    5. Olaizola, Norma & Valenciano, Federico, 2013. "Network formation under linking constraints," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 5194-5205.
    6. Breitmoser, Yves & Vorjohann, Pauline, 2013. "Efficient structure of noisy communication networks," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 396-409.
    7. Rêgo, Leandro Chaves & dos Santos, Andrea Maria, 2019. "Co-authorship model with link strength," European Journal of Operational Research, Elsevier, vol. 272(2), pages 587-594.
    8. 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.
    9. Harmsen - van Hout, Marjolein J.W. & Herings, P. Jean-Jacques & Dellaert, Benedict G.C., 2013. "Communication network formation with link specificity and value transferability," European Journal of Operational Research, Elsevier, vol. 229(1), pages 199-211.
    10. 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.
    11. Haller, Hans & Hoyer, Britta, 2019. "The common enemy effect under strategic network formation and disruption," Journal of Economic Behavior & Organization, Elsevier, vol. 162(C), pages 146-163.
    12. Haller, Hans, 2012. "Network extension," Mathematical Social Sciences, Elsevier, vol. 64(2), pages 166-172.
    13. Dev, Pritha, 2010. "Choosing `Me' and `My Friends': Identity in a Non-Cooperative Network Formation Game with Cost Sharing," MPRA Paper 21631, University Library of Munich, Germany.
    14. Dotan Persitz, 2009. "Power in the Heterogeneous Connections Model: The Emergence of Core-Periphery Networks," Working Papers 2009.42, Fondazione Eni Enrico Mattei.
    15. Cui, Zhiwei & Wang, Shouyang & Zhang, Jin & Zu, Lei, 2013. "Stochastic stability in one-way flow networks," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 410-421.
    16. repec:ehu:ikerla:6411 is not listed on IDEAS
    17. Norma Olaizola & Federico Valenciano, 2014. "One-way flow network formation under constraints," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 624-643, July.
    18. Tenev, Anastas P., 2024. "“Friends Are Thieves of Time”: Heuristic attention sharing in stable friendship networks," Journal of Economic Behavior & Organization, Elsevier, vol. 224(C), pages 785-809.
    19. Ping Sun & Elena Parilina, 2022. "Impact of Utilities on the Structures of Stable Networks with Ordered Group Partitioning," Dynamic Games and Applications, Springer, vol. 12(4), pages 1131-1162, December.
    20. Jackson, Matthew O. & Zenou, Yves, 2015. "Games on Networks," Handbook of Game Theory with Economic Applications,, Elsevier.
    21. Gao Hongwei & Qiao Han & Sedakov Artem & Wang Lei, 2015. "A Dynamic Formation Procedure of Information Flow Networks," Journal of Systems Science and Information, De Gruyter, vol. 3(2), pages 97-110, April.
    22. Yangbo Song & Mihaela Schaar, 2015. "Dynamic network formation with incomplete information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(2), pages 301-331, June.
    23. Francesco Feri & Miguel Meléndez-Jiménez, 2013. "Coordination in evolving networks with endogenous decay," Journal of Evolutionary Economics, Springer, vol. 23(5), pages 955-1000, November.

    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:eee:ejores:v:237:y:2014:i:2:p:566-579. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.