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Payoff Functions In The One-Way Flow Model Of Network Formation For Which Nash Networks Exist

Author

Listed:
  • JEAN DERKS

    (Department of Knowledge Engineering, Maastricht University, P. O. Box 616, 6200 MD, Maastricht, the Netherlands)

  • MARTIJN TENNEKES

    (Department of Knowledge Engineering, Maastricht University, P. O. Box 616, 6200 MD, Maastricht, the Netherlands)

Abstract

We study a non-cooperative model of unilateral network formation. Derkset al.[2008b] prove the existence of local-Nash and global-Nash networks for games with payoff functions that satisfy a framework of axiomatic properties. These properties are inspired by the one-way flow model, which is characterized by the following payoff structure. Each agent pays a cost for each formed link and receives profits from being connect to other agents. In this paper we fully characterize the payoff functions in the one-way flow model that satisfy all properties. We show that under certain conditions, payoff functions with heterogeneous link costs and heterogeneous profits satisfy all properties for which the existence of local-Nash networks is proved. Furthermore, we show that all payoff functions with owner-homogeneous link costs and heterogeneous profits satisfy all properties, and therefore imply the existence of global-Nash networks.

Suggested Citation

  • Jean Derks & Martijn Tennekes, 2011. "Payoff Functions In The One-Way Flow Model Of Network Formation For Which Nash Networks Exist," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 13(01), pages 61-73.
    • Handle: RePEc:wsi:igtrxx:v:13:y:2011:i:01:n:s0219198911002848
    DOI: 10.1142/S0219198911002848
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    References listed on IDEAS

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    1. Demange,Gabrielle & Wooders,Myrna (ed.), 2005. "Group Formation in Economics," Cambridge Books, Cambridge University Press, number 9780521842716, October.
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    More about this item

    Keywords

    Non-cooperative games; network formation; axiomatization; payoff functions; Subject Classification: C72; Subject Classification: D85;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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