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Good neighbors are hard to find: computational complexity of network formation

Author

Listed:
  • Richard Baron

    (CREUSET - Centre de Recherche Economique de l'Université de Saint-Etienne - UJM - Université Jean Monnet - Saint-Étienne)

  • Jacques Durieu

    (CREUSET - Centre de Recherche Economique de l'Université de Saint-Etienne - UJM - Université Jean Monnet - Saint-Étienne)

  • Hans Haller

    (Department of economics - Virginia Polytechnic Institute and State University [Blacksburg])

  • Philippe Solal

    (CREUSET - Centre de Recherche Economique de l'Université de Saint-Etienne - UJM - Université Jean Monnet - Saint-Étienne)

  • Savani Rahul

    (Department of Computer Science [Warwick] - University of Warwick [Coventry])

Abstract

We investigate the computational complexity of several decision problems in a simple strategic game of network formation.We find that deciding if a player has a strategy that guarantees him a certain payoff against a given strategy profile of the other players is an NP-complete problem. Deciding if there exists a strategy profile that guarantees a certain aggregate payoff is also NP-complete. Deciding if there is a Nash equilibrium in pure strategies which guarantees a certain payoff to each player is NP-hard. The problem of deciding if a given strategy profile is a Nash equilibrium is investigated as well.

Suggested Citation

  • Richard Baron & Jacques Durieu & Hans Haller & Philippe Solal & Savani Rahul, 2008. "Good neighbors are hard to find: computational complexity of network formation," Post-Print hal-00268851, HAL.
    • Handle: RePEc:hal:journl:hal-00268851
    DOI: 10.1007/s10058-008-0043-x
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    References listed on IDEAS

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    1. Koller, Daphne & Megiddo, Nimrod & von Stengel, Bernhard, 1996. "Efficient Computation of Equilibria for Extensive Two-Person Games," Games and Economic Behavior, Elsevier, vol. 14(2), pages 247-259, June.
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    4. Haller, Hans & Sarangi, Sudipta, 2005. "Nash networks with heterogeneous links," Mathematical Social Sciences, Elsevier, vol. 50(2), pages 181-201, September.
    5. Berninghaus, Siegfried K. & Schwalbe, Ulrich, 1996. "Evolution, interaction, and Nash equilibria," Journal of Economic Behavior & Organization, Elsevier, vol. 29(1), pages 57-85, January.
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    Cited by:

    1. Demuynck, Thomas, 2011. "The computational complexity of rationalizing boundedly rational choice behavior," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 425-433.
    2. Gilles, Robert P. & Chakrabarti, Subhadip & Sarangi, Sudipta, 2012. "Nash equilibria of network formation games under consent," Mathematical Social Sciences, Elsevier, vol. 64(2), pages 159-165.
    3. Thomas Demuynck, 2014. "The computational complexity of rationalizing Pareto optimal choice behavior," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(3), pages 529-549, March.
    4. Sung, Shao-Chin & Dimitrov, Dinko, 2010. "Computational complexity in additive hedonic games," European Journal of Operational Research, Elsevier, vol. 203(3), pages 635-639, June.
    5. Rahmi İlkılıç & Hüseyin İkizler, 2019. "Equilibrium refinements for the network formation game," Review of Economic Design, Springer;Society for Economic Design, vol. 23(1), pages 13-25, June.
    6. Fabrice Talla Nobibon & Laurens Cherchye & Yves Crama & Thomas Demuynck & Bram De Rock & Frits C. R. Spieksma, 2016. "Revealed Preference Tests of Collectively Rational Consumption Behavior: Formulations and Algorithms," Operations Research, INFORMS, vol. 64(6), pages 1197-1216, December.

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    More about this item

    Keywords

    Strategic games · Network formation · Computational complexity;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D02 - Microeconomics - - General - - - Institutions: Design, Formation, Operations, and Impact
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

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