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Essential stability of cooperative equilibria for population games

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Abstract

In this paper, we first introduce the notion of cooperative equilibria for population games and prove its existence theorem by Proposition 2 in Kajii (J Econ Theory 56:194–205, 1992). We next identify a residual dense subclass of population games whose cooperative equilibria are all essential. Moreover, we show the existence of essential components of the cooperative equilibrium set by proving the connectivity of minimal essential sets of the cooperative equilibrium set.

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Acknowledgements

This study was funded by National Natural Science Foundation of China (Grant Number 11501349), and Graduate Innovation Foundation sponsored by Shanghai University of Finance and Economics (Grant Number CXJJ-2018-355).

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Authors and Affiliations

  1. School of Economics, Shanghai University of Finance and Economics, Shanghai, 200433, People’s Republic of China

    Zhe Yang & Haiqun Zhang

  2. Key Laboratory of Mathematical Economics (SUFE), Ministry of Education, Shanghai, 200433, People’s Republic of China

    Zhe Yang & Haiqun Zhang

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  1. Zhe Yang
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  2. Haiqun Zhang
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Correspondence to Zhe Yang.

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Yang, Z., Zhang, H. Essential stability of cooperative equilibria for population games. Optim Lett 13, 1573–1582 (2019). https://doi.org/10.1007/s11590-018-1303-5

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