  We study a portfolio management problem featuring many-player and mean field
competition, investment and consumption, and relative performance concerns
under the forward performance processes (FPP) framework. We focus on agents
using power (CRRA) type FPPs for their investment-consumption optimization
problem under a common noise Merton market model. We solve both the many-player
and mean field game providing closed-form expressions for the solutions where
the limit of the former yields the latter. In our case, the FPP framework
yields a continuum of solutions for the consumption component as indexed to a
market parameter we coin "market-risk relative consumption preference". The
parameter permits the agent to set a preference for their consumption going
forward in time that, in the competition case, reflects a common market
behaviour. We show the FPP framework, under both competition and
no-competition, allows the agent to disentangle her risk-tolerance and
elasticity of intertemporal substitution (EIS) just like Epstein-Zin
preferences under recursive utility framework and unlike the classical utility
theory one. This, in turn, allows a finer analysis on the agent's consumption
"income" and "substitution" regimes, and, of independent interest, motivates a
new strand of economics research on EIS under the FPP framework. We find that
competition rescales the agent's perception of consumption in a non-trivial
manner. We provide numerical illustrations of our results.
