Skip to main content
SpringerLink
Log in

The Calculation and Simulation of the Price of Anarchy for Network Formation Games

  • Research
  • Published:
Networks and Spatial Economics Aims and scope Submit manuscript

Abstract

We model the formation of networks as the result of a game where by players act selfishly to get the portfolio of links they desire most. The integration of player strategies into the network formation model is appropriate for organizational networks because in these smaller networks, dynamics are not random, but the result of intentional actions carried through by players maximizing their own objectives. This model is a better framework for the analysis of influences upon a network because it integrates the strategies of the players involved. We present an Integer Program that calculates the price of anarchy of this game by finding the worst stable graph and the best coordinated graph for this game. We simulate the formation of the network and calculated the simulated price of anarchy, which we find tends to be rather low.

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
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Data Availability

Material use in the creation of this paper may be accessed by contacting the corresponding author.

References

  • Albert R, Barabási AL (2002) Statistical mechanics of complex networks. Rev Modern Phys 74(1):47–97

    Article  Google Scholar 

  • Asur S, Huberman BA (2010) Predicting the future with social media. Technical Report. http://arxiv.org/abs/1003.5699v1

  • Backstrom L, Dwork C, Kleinberg J (2007) Wherefore art thou r3579x? Anonymized social networks, hidden patterns and structural steganography. In: Proceedings of the 16th World Wide Web Conference

  • Bala V, Goyal S (2000) A noncooperative model of network formation. Econometrica 68(5):1181–1229

    Article  Google Scholar 

  • Barabasi AL, Albert R (1999) Emergence of scaling in random networks. Science 286(5439):509

    Article  Google Scholar 

  • Belleflamme P, Bloch F (2004) Market sharing agreements and collusive networks. Int Econ Rev 45(2):387–411

    Article  Google Scholar 

  • Britton T, Deijfen M, Martin-Löf A (2006) Generating simple random graphs with prescribed degree distribution. J Stat Phys 124(6):1377–1397

    Article  Google Scholar 

  • Carrington PJ, Scott J, Wasserman S (2005) Models and methods in social network analysis. Cambridge University Press

    Book  Google Scholar 

  • Christodoulou G, Koutsoupias E (2005) The price of anarchy of finite congestion games. In: Proceedings of the Thirty-seventh Annual ACM Symposium on Theory of Computing. STOC ’05, pp 67–73. ACM, New York, NY, USA. https://doi.org/10.1145/1060590.1060600

  • Del Genio CI, Kim H, Toroczkai Z, Bassler KE (2010) Efficient and exact sampling of simple graphs with given arbitrary degree sequence. PLoS One 5(4):10012

    Article  Google Scholar 

  • Diestel R (2010) Graph Theory, 4th edn. Graduate Texts in Mathematics. Springer, Berlin

    Book  Google Scholar 

  • Dorogovtsev SN, Mendes JFF (2002) Evolution of networks. Adv Phys 51(4):1079–1187

    Article  Google Scholar 

  • Doyle JC, Alderson DL, Li L, Low S, Roughan M, Shalunov S, Tanaka R, Willinger W (2005) The robust yet fragile nature of the Internet. Proc Natl Acad Sci USA 102(41):14497

    Article  Google Scholar 

  • Dozier K (2011) CIA following Twitter, Facebook. Associated Press: http://news.yahoo.com/ap-exclusive-cia-following-twitter-facebook-081055316.html

  • Dubey P (1986) Inefficiency of Nash equilibria. Math Oper Res 1–8

  • Dutta B, Mutuswami S (1997) Stable networks. J Econ Theory 76(2):322–344

    Article  Google Scholar 

  • Facchinei F, Fischer A, Piccialli V (2007) On generalized Nash games and variational inequalities. Oper Res Lett 35:159–164

    Article  Google Scholar 

  • Friggeri A, Chelius G, Fleury E (2011) Fellows: Crowd-sourcing the evaluation of an overlapping community model based on the cohesion measure. In: Proceedings of the Interdisciplinary Workshop on Information and Decision in Social Networks, Massachusetts Institute of Technology. Laboratory for Information and Decision Systems

  • Griffin C, Testa K, Racunas S (2011) An algorithm for searching an alternative hypothesis space. IEEE Trans Sys Man Cyber B 41(3):772–782

    Article  Google Scholar 

  • Godsil C, Royle G (2001) Algebraic Graph Theory. Springer, Berlin

    Book  Google Scholar 

  • Goyal S, Joshi S (2003) Networks of collaboration in oligopoly. Games Econ Behav 43(1):57–85

    Article  Google Scholar 

  • Goyal S, Joshi S (2006) Unequal connections. Int J Game Theory 34(3):319–349

    Article  Google Scholar 

  • Gross J, Yellen J (2005) Graph Theory and Its Applications, 2nd edn. CRC Press, Boca Raton, FL, USA

    Book  Google Scholar 

  • Jackson MO (2003) A survey of models of network formation: Stability and efficiency. Game Theory and Information

  • Jackson MO (2008) Social and Economic Networks. Princeton University Press, Princeton, NJ

    Book  Google Scholar 

  • Jackson MO, Van Den Nouweland A (2005) Strongly stable networks. Games Econ Behav 51(2):420–444

    Article  Google Scholar 

  • Jackson MO, Wolinsky A (1996) A strategic model of social and economic networks. J Econ Theory 71(1):44–74

    Article  Google Scholar 

  • Jin EM, Girvan M, Newman MEJ (2001) Structure of growing social networks. Phys Rev 64:046132

    Google Scholar 

  • Knoke D, Yang S (2008) Social network analysis. Quantitative applications in the social sciences, vol. 154. SAGE Publications

  • Koutsoupias E, Papadimitriou CH (1999) Worst-case equilibria. In: Proceedings of STACS 99

  • Lichter S, Griffin C, Friesz T (2011) A game theoretic perspective on network topologies. Submitted to Computational and Mathematical Organization Theory (under revision). http://arxiv.org/abs/1106.2440

  • Lichter S, Griffin C, Friesz T (2011) Link biased strategies in network formation games. In: Proceedings of the 3rd IEEE Conference on Social Computing, MIT, Boston, MA

  • Mihail M, Vishnoi NK (2002) On generating graphs with prescribed vertex degrees for complex network modeling. ARACNE 2002:1–11

    Google Scholar 

  • Milo R, Kashtan N, Itzkovitz S, Newman M, Alon U (2003) On the uniform generation of random graphs with prescribed degree sequences. Arxiv preprint: cond-mat/0312028

  • Myerson RB (1977) Graphs and cooperation in games. Math Oper Res 2(3):225–229

    Article  Google Scholar 

  • Newman M (2003) The structure and function of complex networks. SIAM Rev 45:167–256

    Article  Google Scholar 

  • Olshevsky A, Tsitsiklis JN (2011) Convergence speed in distributed consensus and averaging. SIAM Rev 53(4):747–772

    Article  Google Scholar 

  • Rosenthal RW (1973) A class of games possessing pure-strategy Nash equilibria. Int J Game Theory 2:65–67. https://doi.org/10.1007/BF01737559

    Article  Google Scholar 

  • Squicciarini AC, Sundareswaran S, Griffin C (2011) A game theoretical perspective of users’ registration in online social platforms. In: Accepted to Third IEEE International Conference on Privacy, Security, Risk and Trust

  • Yang WS, Dia JB (2008) Discovering cohesive subgroups from social networks for targeted advertising. Exp Syst Appl 34(3):2029–2038

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fraud Analytics, Morgan Stanley, 1300 Thames St., Baltimore, 21231, MD, USA

    Shaun Lichter

  2. Applied Research Laboratory, Penn State University, P.O. Box 30, State College, 16804-0030, PA, USA

    Christopher Griffin

  3. Harold and Inge Marcus Department of Industrial and Manufacturing Engineering, Penn State University, University Park, 16802, PA, USA

    Terry Friesz

Authors
  1. Shaun Lichter
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christopher Griffin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Terry Friesz
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed to analysis, writing and editing.

Corresponding author

Correspondence to Terry Friesz.

Ethics declarations

Ethical Approval

Not applicable.

Competing Interests

The authors declare no competing interests.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lichter, S., Griffin, C. & Friesz, T. The Calculation and Simulation of the Price of Anarchy for Network Formation Games. Netw Spat Econ 23, 581–610 (2023). https://doi.org/10.1007/s11067-023-09588-x

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11067-023-09588-x

Keywords

Search

Navigation