  In It\^{o}-diffusion environments, we introduce and analyze $N$-player and
common-noise mean-field games in the context of optimal portfolio choice in a
common market. The players invest in a finite horizon and also interact, driven
either by competition or homophily. We study an incomplete market model in
which the players have constant individual risk tolerance coefficients (CARA
utilities). We also consider the general case of random individual risk
tolerances and analyze the related games in a complete market setting. This
randomness makes the problem substantially more complex as it leads to ($N$ or
a continuum of) auxiliary ''individual'' It\^{o}-diffusion markets. For all
cases, we derive explicit or closed-form solutions for the equilibrium
stochastic processes, the optimal state processes, and the values of the games.
