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Bonacich Measures as Equilibria in Network Models

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  • Hannu Salonen

    (Department of Economics, University of Turku)

Abstract

We investigate the cases when the Bonacich measures of strongly connected directed bipartite networks can be interpreted as a Nash equilibrium of a non-cooperative game. One such case is a two-person game such that the utility functions are bilinear, the matrices of these bilinear forms represent the network, and strategies have norm at most one. Another example is a two-person game with quadratic utility functions. A third example is an m + n person game with quadratic utilitity functions, where the matrices representing the network have dimension m × n. For connected directed bipartite networks we show that the Bonacich measures are unique and give a recursion formula for the computation of the measures. The Bonacich measures of such networks can be interpreted as a subgame perfect equilibrium path of an extensive form game with almost perfect information.

Suggested Citation

  • Hannu Salonen, 2015. "Bonacich Measures as Equilibria in Network Models," Discussion Papers 100, Aboa Centre for Economics.
    • Handle: RePEc:tkk:dpaper:dp100
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    References listed on IDEAS

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    4. Hannu Salonen, 2016. "Equilibria and centrality in link formation games," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 1133-1151, November.
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    Cited by:

    1. Salonen Hannu, 2016. "Bonacich Network Measures as Minimum Norm Solutions," Discussion Papers 106, Aboa Centre for Economics.

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    More about this item

    Keywords

    networks; influence measures; Nash equilibrium;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

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