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Inverse Stackelberg Public Goods Game with Multiple Hierarchies Under Global and Local Information Structures

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Abstract

This paper studies the inverse Stackelberg game with multiple hierarchies under global and local information structures, where the players have discrete strategy spaces. For the classic public goods game, we solve the pure-strategy inverse Stackelberg equilibria under three typical hierarchical structures. The results reveal some counterintuitive characteristics within the systems with hierarchies, such as that the cooperation does not increase with the return rate at the equilibria. Furthermore, by defining a local information structure, we give an estimate of the fewest hierarchies required for full cooperation, which can be a constant multiple of the logarithm or square root of the population size or of the population size itself, according to different information structures and return rates. This paper proposes a novel mechanism to play the game and promote cooperation. Both the formulation and analysis method are different from existing works, and the results can find their ample implications in practice, which might help decision making in hierarchical systems.

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Acknowledgements

The author thanks Professor Lei Guo in AMSS, CAS, for his inspiring help through the paper.

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Authors and Affiliations

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Yifen Mu

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  1. Yifen Mu
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Correspondence to Yifen Mu.

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Communicated by Qianchuan Zhao.

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Mu, Y. Inverse Stackelberg Public Goods Game with Multiple Hierarchies Under Global and Local Information Structures. J Optim Theory Appl 163, 332–350 (2014). https://doi.org/10.1007/s10957-013-0475-5

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  • DOI: https://doi.org/10.1007/s10957-013-0475-5

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