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

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

International Journal of Business and Economic Sciences Applied Research (IJBESAR), 2013, vol. 6, issue 3, 79-96

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.

Keywords: social network; asymmetric game; mixed-strategy equilibrium; independence; uniqueness (search for similar items in EconPapers)
JEL-codes: C62 C72 (search for similar items in EconPapers)
Date: 2013
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