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Forward-looking Pairwise Stability in Networks with Externalities

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  • Navarro Prada, Noemí

Abstract

We consider cooperation situations where players have network relations. Networks evolve according to a stationary transition probability matrix and at each moment in time players receive payoffs from a stationary allocation rule. Players discount the future by a common factor. The pair formed by an allocation rule and a transition probability matrix is called a forward-looking network formation scheme if, first, the probability that a link is created is positive if the discounted, expected gains to its two participants are positive, and if, second, the probability that a link is eliminated is positive if the discounted, expected gains to at least one of its two participants are positive. The main result is the existence, for all discount factors and all value functions, of a forward-looking network formation scheme. Furthermore, we can always nd a forward-looking network formation scheme such that (i) the allocation rule is component balanced and (ii) the transition probabilities increase in the di erence in payo s for the corresponding players responsible for the transition. We use this dynamic solution concept to explore the tension between e ciency and stability.

Suggested Citation

  • Navarro Prada, Noemí, 2013. "Forward-looking Pairwise Stability in Networks with Externalities," IKERLANAK Ikerlanak;2013-71, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
  • Handle: RePEc:ehu:ikerla:10331
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    File URL: https://addi.ehu.es/handle/10810/10331
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    References listed on IDEAS

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    1. Sergio Currarini & Massimo Morelli, 2000. "Network Formation with Sequential Demands," Royal Holloway, University of London: Discussion Papers in Economics 99/2, Department of Economics, Royal Holloway University of London, revised Feb 2000.
    2. Slikker, Marco & van den Nouweland, Anne, 2001. "A One-Stage Model of Link Formation and Payoff Division," Games and Economic Behavior, Elsevier, vol. 34(1), pages 153-175, January.
    3. Dutta, Bhaskar & Ghosal, Sayantan & Ray, Debraj, 2005. "Farsighted network formation," Journal of Economic Theory, Elsevier, vol. 122(2), pages 143-164, June.
    4. Noemí Navarro, 2014. "Expected fair allocation in farsighted network formation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(2), pages 287-308, August.
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    Cited by:

    1. Carayol, Nicolas & Delille, Rémy & Vannetelbosch, Vincent, 2015. "Allocating value among farsighted players in network formation," Economics Letters, Elsevier, vol. 137(C), pages 50-53.

    More about this item

    Keywords

    allocation rules for networks; Markov chain; strategic network formation; pairwise stability;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other

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