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

Author

Listed:
  • Shaun Lichter

    (Morgan Stanley)

  • Christopher Griffin

    (Penn State University)

  • Terry Friesz

    (Penn State University)

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.

Suggested Citation

  • Shaun Lichter & Christopher Griffin & Terry Friesz, 2023. "The Calculation and Simulation of the Price of Anarchy for Network Formation Games," Networks and Spatial Economics, Springer, vol. 23(3), pages 581-610, September.
    • Handle: RePEc:kap:netspa:v:23:y:2023:i:3:d:10.1007_s11067-023-09588-x
    DOI: 10.1007/s11067-023-09588-x
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    References listed on IDEAS

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    1. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    2. Goyal, Sanjeev & Joshi, Sumit, 2003. "Networks of collaboration in oligopoly," Games and Economic Behavior, Elsevier, vol. 43(1), pages 57-85, April.
    3. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
    4. Paul Belleflamme & Francis Bloch, 2004. "Market sharing agreements and collusive networks," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(2), pages 387-411, May.
    5. Charo I Del Genio & Hyunju Kim & Zoltán Toroczkai & Kevin E Bassler, 2010. "Efficient and Exact Sampling of Simple Graphs with Given Arbitrary Degree Sequence," PLOS ONE, Public Library of Science, vol. 5(4), pages 1-7, April.
    6. Emily M. Jin & Michelle Girvan & M. E. J. Newman, 2001. "The Structure of Growing Social Networks," Working Papers 01-06-032, Santa Fe Institute.
    7. Matthew O. Jackson, 2003. "A survey of models of network formation: Stability and efficiency," Working Papers 1161, California Institute of Technology, Division of the Humanities and Social Sciences.
    8. Goyal, Sanjeev & Joshi, Sumit, 2003. "Networks of collaboration in oligopoly," Games and Economic Behavior, Elsevier, vol. 43(1), pages 57-85, April.
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