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Mean Field Games for Stochastic Growth with Relative Utility

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Abstract

This paper considers continuous time stochastic growth-consumption optimization in a mean field game setting. The individual capital stock evolution is determined by a Cobb–Douglas production function, consumption and stochastic depreciation. The individual utility functional combines an own utility and a relative utility with respect to the population. The use of the relative utility reflects human psychology, leading to a natural pattern of mean field interaction. The fixed point equation of the mean field game is derived with the aid of some ordinary differential equations. Due to the relative utility interaction, our performance analysis depends on some ratio based approximation error estimate.

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Acknowledgements

The authors gratefully thank an anonymous referee for suggesting a simplified proof of Proposition 12 and an improved error estimate in Theorem 10.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Carleton University, Ottawa, ON, K1S 5B6, Canada

    Minyi Huang

  2. Department of Mathematics, University of Puerto Rico, San Juan, PR, 00936, USA

    Son Luu Nguyen

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  1. Minyi Huang
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  2. Son Luu Nguyen
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Correspondence to Minyi Huang.

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Huang, M., Nguyen, S.L. Mean Field Games for Stochastic Growth with Relative Utility. Appl Math Optim 74, 643–668 (2016). https://doi.org/10.1007/s00245-016-9395-8

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