Skip to main content
SpringerLink
Log in

Myopic-farsighted absorbing networks

  • Published:
Theory and Decision Aims and scope Submit manuscript

Abstract

We propose the notion of myopic-farsighted absorbing set to determine the networks that emerge in the long run when some players are myopic while others are farsighted. A set of networks is a myopic-farsighted absorbing set if (No External Deviation) there is no myopic-farsighted improving path from networks within the set to some networks outside the set, (External Stability) there is a myopic-farsighted improving path from any network outside the set to some network within the set, and (Minimality) there is no proper subset satisfying No External Deviation and External Stability. Contrary to the notion of myopic-farsighted stable set, we show that a myopic-farsighted absorbing set always exists. We partially characterize the myopic-farsighted absorbing sets and we provide sufficient conditions for the equivalence between a myopic-farsighted absorbing set and a myopic-farsighted stable set. We also introduce and fully characterize the notion of proper myopic-farsighted absorbing set that refines the concept of myopic-farsighted absorbing set by selecting the more absorbing networks. Finally, we consider a threshold game that illustrates the role of the relative number of farsighted and myopic players for reaching efficiency.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Notes

  1. Mauleon and Vannetelbosch (2016) provide a comprehensive overview of the solution concepts for solving network formation games.

  2. Jackson and Watts (2002) study a dynamic, but myopic, network formation process in which agents form and sever links based on the improvement that the resulting network offers them relative to the current network. See also Tercieux and Vannetelbosch (2006).

  3. Throughout the paper we use the notation \(\subseteq \) for weak inclusion and \(\varsubsetneq \) for strict inclusion. Finally, \(\#\) will refer to the notion of cardinality.

  4. Page and Wooders (2009) define a basin of attraction as a set of networks to which the network formation process might tend and from which there is no escape.

  5. Herings et al. (2020) define first the myopic-farsighted stable set for two-sided matching problems, and Mauleon et al. (2018) extend it to R&D network formation with pairwise deviations.

  6. Alternative notions of farsightedness are suggested by Chwe (1994), Diamantoudi and Xue (2003), Dutta and Vohra (2017), Herings et al. (2004), Herings et al. (2019), Mauleon and Vannetelbosch (2004), Page et al. (2005), Ray and Vohra (2019), Xue (1998) among others.

  7. The pairwise CP vNM set follows the approach by Page and Wooders (2009) who define the stable set with respect to path dominance, i.e., the transitive closure of \(\phi \).

  8. Luo et al. (2021) provide conditions on the utility function that guarantee the existence and uniqueness of a myopic-farsighted stable set.

References

  • Chwe, M. S. (1994). Farsighted coalitional stability. Journal of Economic Theory, 63, 299–325.

    Article  Google Scholar 

  • Diamantoudi, E., & Xue, L. (2003). Farsighted stability in hedonic games. Social Choice and Welfare, 21, 39–61.

    Article  Google Scholar 

  • Dutta, B., Ghosal, S., & Ray, R. (2005). Farsighted network formation. Journal of Economic Theory, 122, 143–164.

    Article  Google Scholar 

  • Dutta, B., & Vohra, R. (2017). Rational expectations and farsighted stability. Theoretical Economics, 12, 1191–1227.

    Article  Google Scholar 

  • Herings, P. J. J., Mauleon, A., & Vannetelbosch, V. (2004). Rationalizability for social environments. Games and Economic Behavior, 49, 135–156.

    Article  Google Scholar 

  • Herings, P. J. J., Mauleon, A., & Vannetelbosch, V. (2009). Farsightedly stable networks. Games and Economic Behavior, 67, 526–541.

    Article  Google Scholar 

  • Herings, P. J. J., Mauleon, A., & Vannetelbosch, V. (2017). Stable sets in matching problems with coalitional sovereignty and path dominance. Journal of Mathematical Economics, 71, 14–19.

    Article  Google Scholar 

  • Herings, P. J. J., Mauleon, A., & Vannetelbosch, V. (2019). Stability of networks under horizon-\(K\) farsightedness. Economic Theory, 68, 177–200.

    Article  Google Scholar 

  • Herings, P. J. J., Mauleon, A., & Vannetelbosch, V. (2020). Matching with myopic and farsighted players. Journal of Economic Theory, 190, 105125.

    Article  Google Scholar 

  • Jackson, M. O. (2008). Social and economic networks. Princeton, NJ, USA: Princeton University Press.

    Book  Google Scholar 

  • Jackson, M. O., & Watts, A. (2002). The evolution of social and economic networks. Journal of Economic Theory, 106, 265–295.

    Article  Google Scholar 

  • Jackson, M. O., & Wolinsky, A. (1996). A strategic model of social and economic networks. Journal of Economic Theory, 71, 44–74.

    Article  Google Scholar 

  • Kirchsteiger, G., Mantovani, M., Mauleon, A., & Vannetelbosch, V. (2016). Limited farsightedness in network formation. Journal of Economic Behavior and Organization, 128, 97–120.

    Article  Google Scholar 

  • Luo, C., Mauleon, A., & Vannetelbosch, V. (2021). Network formation with myopic and farsighted players. Economic Theory, 71, 1283–1317.

    Article  Google Scholar 

  • Mauleon, A., Sempere-Monerris, J.J., & Vannetelbosch, V. (2018). R&D network formation with myopic and farsighted firms. CORE Discussion Paper 2018-26, UCLouvain.

  • Mauleon, A., & Vannetelbosch, V. (2004). Farsightedness and cautiousness in coalition formation games with positive spillovers. Theory and Decision, 56, 291–324.

    Article  Google Scholar 

  • Mauleon, A., & Vannetelbosch, V. (2016). Network formation games. In Y. Bramoullé, A. Galeotti, & B. W. Rogers (Eds.), The Oxford Handbook of The Economics of Networks. UK: Oxford University Press.

    Google Scholar 

  • Page, F. H., Jr., & Wooders, M. (2009). Strategic basins of attraction, the path dominance core, and network formation games. Games and Economic Behavior, 66, 462–487.

    Article  Google Scholar 

  • Page, F. H., Jr., Wooders, M., & Kamat, S. (2005). Networks and farsighted stability. Journal of Economic Theory, 120, 257–269.

    Article  Google Scholar 

  • Ray, D., & Vohra, R. (2015). The farsighted stable set. Econometrica, 83(3), 977–1011.

    Article  Google Scholar 

  • Ray, D., & Vohra, R. (2019). Maximality in the farsighted stable set. Econometrica, 87(5), 1763–1779.

    Article  Google Scholar 

  • Tercieux, O., & Vannetelbosch, V. (2006). A characterization of stochastically stable networks. International Journal of Game Theory, 34, 351–369.

    Article  Google Scholar 

  • Teteryatnikova, M., & Tremewan, J. (2020). Myopic and farsighted stability in network formation games: an experimental study. Economic Theory, 69, 987–1021.

    Article  Google Scholar 

  • Xue, L. (1998). Coalitional stability under perfect foresight. Economic Theory, 11, 603–627.

    Article  Google Scholar 

Download references

Acknowledgements

Ana Mauleon and Vincent Vannetelbosch are, respectively, Research Director and Senior Research Associate of the National Fund for Scientific Research (FNRS). Financial support from the Fonds de la Recherche Scientifique - FNRS research grant T.0143.18 is gratefully acknowledged.

Author information

Authors and Affiliations

  1. CORE/LIDAM, UCLouvain, Louvain-la-Neuve; CEREC, UCLouvain Saint-Louis, Brussels, Belgium

    Pierre de Callataÿ

  2. CEREC, UCLouvain Saint-Louis, Brussels; CORE/LIDAM, UCLouvain, Louvain-la-Neuve, Belgium

    Ana Mauleon

  3. CORE/LIDAM, UCLouvain, Louvain-la-Neuve, Belgium

    Vincent Vannetelbosch

Authors
  1. Pierre de Callataÿ
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ana Mauleon
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Vincent Vannetelbosch
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vincent Vannetelbosch.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

de Callataÿ, P., Mauleon, A. & Vannetelbosch, V. Myopic-farsighted absorbing networks. Theory Decis 94, 405–422 (2023). https://doi.org/10.1007/s11238-022-09895-8

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11238-022-09895-8

Keywords

Search

Navigation