A Mean Field Capital Accumulation Game with HARA Utility

作者：Huang Minyi^*

来源：Dynamic Games and Applications, 2013, 3(4): 446-472.

DOI：10.1007/s13235-013-0092-9

• Stochastic growth
• Investment
• Consumption
• Externality
• Mean field approximation
• Nash equilibrium
• Out-of-equilibrium behavior

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%26apos;s sensitivity to the mean field.

• 出版日期2013-12