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Existence of Nash Networks and Partner Heterogeneity

Author

Listed:
  • Pascal Billand

    (GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - ENS de Lyon - École normale supérieure de Lyon - Université de Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique)

  • Christophe Bravard

    (GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - ENS de Lyon - École normale supérieure de Lyon - Université de Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique)

  • Sudipta Sarangi

    (Department of Economics, Louisiana State University - LSU - Louisiana State University [BatonRouge])

Abstract

In this paper, we pursue the line of research initiated by Haller and Sarangi (2005). We examine the existence of equilibrium networks called Nash networks in the non-cooperative two-way flow model by [Bala and Goyal, 2000a] and [Bala and Goyal, 2000b] in the presence of partner heterogeneity. First, we show through an example that Nash networks in pure strategies do not always exist in such model. We then impose restrictions on the payoff function to find conditions under which Nash networks always exist. We provide two properties--increasing differences and convexity in the first argument of the payoff function that ensure the existence of Nash networks. Note that the commonly used linear payoff function satisfies these two properties.

Suggested Citation

  • Pascal Billand & Christophe Bravard & Sudipta Sarangi, 2012. "Existence of Nash Networks and Partner Heterogeneity," Post-Print halshs-00728035, HAL.
    • Handle: RePEc:hal:journl:halshs-00728035
    DOI: 10.1016/j.mathsocsci.2012.01.001
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    Cited by:

    1. Ping Sun & Elena Parilina, 2024. "Networks with nonordered partitioning of players: stability and efficiency with neighborhood-influenced cost topology," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 99(3), pages 271-305, June.
    2. Charoensook, Banchongsan, "undated". "On the Interaction between Player Heterogeneity and Partner Heterogeneity in Two-way Flow Strict Nash Networks," Climate Change and Sustainable Development 204844, Fondazione Eni Enrico Mattei (FEEM).
    3. Charoensook, Banchongsan, 2015. "On the Interaction between Player Heterogeneity and Partner Heterogeneity in Strict Nash Networks," MPRA Paper 61205, University Library of Munich, Germany.
    4. Banchongsan Charoensook, 2020. "On the Interaction between Small Decay, Agent Heterogeneity and Diameter of Minimal Strict Nash Networks in Two-way Flow Model," Annals of Economics and Finance, Society for AEF, vol. 21(2), pages 331-361, November.
    5. Olaizola, By Norma & Valenciano, Federico, 2021. "Efficiency and stability in the connections model with heterogeneous nodes," Journal of Economic Behavior & Organization, Elsevier, vol. 189(C), pages 490-503.

    More about this item

    Keywords

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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

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