Mean Field Games for Stochastic Growth with Relative Utility

Journal Article · Thu Dec 15 04:00:00 EST 2016 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-016-9395-8· OSTI ID:22617148

Huang, Minyi ^[1]

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1. Carleton University, School of Mathematics and Statistics (Canada)

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.

• OSTI ID: 22617148
• Journal Information: Applied Mathematics and Optimization, Journal Name: Applied Mathematics and Optimization Journal Issue: 3 Vol. 74; ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
APPROXIMATIONS
DEPRECIATION
DIFFERENTIAL EQUATIONS
ERRORS
EVOLUTION
INTERACTIONS
INVENTORIES
MEAN-FIELD THEORY
OPTIMIZATION
PERFORMANCE
STOCHASTIC PROCESSES