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Pairwise-stability and Nash equilibria in network formation

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  • Antoni Calvó-Armengol
  • Rahmi İlkılıç

Abstract

Suppose that individual payoffs depend on the network connecting them. Consider the following simultaneous move game of network formation: players announce independently the links they wish to form, and links are formed only under mutual consent. We provide necessary and sufficient conditions on the network link marginal payoffs such that the set of pairwise stable, pairwise-Nash and proper equilibrium networks coincide, where pairwise stable networks are robust to one-link deviations, while pairwise-Nash networks are robust to one-link creation but multi-link severance. Under these conditions, proper equilibria in pure strategies are fully characterized by one-link deviation checks.
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Suggested Citation

  • Antoni Calvó-Armengol & Rahmi İlkılıç, 2009. "Pairwise-stability and Nash equilibria in network formation," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(1), pages 51-79, March.
    • Handle: RePEc:spr:jogath:v:38:y:2009:i:1:p:51-79
    DOI: 10.1007/s00182-008-0140-7
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    More about this item

    Keywords

    Network formation; Pairwise-stability; Proper equilibrium; C62; C72; D85; L14;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation
    • L14 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Transactional Relationships; Contracts and Reputation

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