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Independence and Uniqueness of the Mixed-Strategy Equilibrium in Social Networks

Author

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  • Darong Dai

    () (Department of Economics, School of Business, Nanjing University, Nanjing 210093, People’s Republic of China)

Abstract

We develop topological analysis of social-network effect on game equilibrium in the context of two- player asymmetric normal-form games and also in evolutionary sense. Firstly, it is confirmed that the game equilibrium in many social networks cannot be established through that in a well-mixed population. In other words, we have proved the independence of the mixedstrategy equilibrium in social networks. Secondly, it is demonstrated that the game equilibrium exhibits injective property with respect to the corresponding social-network effect under consideration. That is, the uniqueness of the mixed-strategy game equilibrium in a given social network is identified. Thirdly, it is argued that uniqueness implies independence for a wide range of social networks and we have even derived the biggest sets of social networks in which independence and uniqueness hold true, respectively, in the underlying game. To sum up, we have provided qualitative characterizations about topological properties of the mixed-strategy game equilibrium in general social networks.

Suggested Citation

  • Darong Dai, 2013. "Independence and Uniqueness of the Mixed-Strategy Equilibrium in Social Networks," International Journal of Business and Economic Sciences Applied Research (IJBESAR), Eastern Macedonia and Thrace Institute of Technology (EMATTECH), Kavala, Greece, vol. 6(3), pages 79-96, December.
  • Handle: RePEc:tei:journl:v:6:y:2013:i:3:p:79-96
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    social network; asymmetric game; mixed-strategy equilibrium; independence; uniqueness;

    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

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