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.

Additional Metadata
Keywords Consumption, Externality, Investment, Mean field approximation, Nash equilibrium, Out-of-equilibrium behavior, Stochastic growth
Persistent URL dx.doi.org/10.1007/s13235-013-0092-9
Journal Dynamic Games and Applications
Citation
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