This paper introduces a mean field modeling framework for consumption-accumulation optimization. The production dynamics are generalized from stochastic growth theory by addressing the collective impact of a large population of similar agents on efficiency. This gives rise to a stochastic dynamic game with mean field coupling in the dynamics, where we adopt a hyperbolic absolute risk aversion (HARA) utility functional for the agents. A set of decentralized strategies is obtained by using the Nash certainty equivalence approach. To examine the long-term behavior we introduce a notion called the relaxed stationary mean field solution. The simple strategy computed from this solution is used to investigate the out-of-equilibrium behavior of the mean field system. Interesting nonlinear phenomena can emerge, including stable equilibria, limit cycles and chaos, which are related to the agent's sensitivity to the mean field.

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Keywords Consumption, Externality, Investment, Mean field approximation, Nash equilibrium, Out-of-equilibrium behavior, Stochastic growth
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Journal Dynamic Games and Applications
Huang, M. (2013). A Mean Field Capital Accumulation Game with HARA Utility. Dynamic Games and Applications, 3(4), 446–472. doi:10.1007/s13235-013-0092-9