  This paper studies an optimal investment-consumption problem for competitive
agents with exponential or power utilities and a common finite time horizon.
Each agent regards the average of habit formation and wealth from all peers as
benchmarks to evaluate the performance of her decision. We formulate the
n-agent game problems and the corresponding mean field game problems under the
two utilities. One mean field equilibrium is derived in a closed form in each
problem. In each problem with n agents, an approximate Nash equilibrium is then
constructed using the obtained mean field equilibrium when n is sufficiently
large. The explicit convergence order in each problem can also be obtained. In
addition, we provide some numerical illustrations of our results.
