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In It\^{o}-diffusion environments, we introduce and analyze $N$-player andcommon-noise mean-field games in the context of optimal portfolio choice in acommon market. The players invest in a finite horizon and also interact, driveneither by competition or homophily. We study an incomplete market model inwhich the players have constant individual risk tolerance coefficients (CARAutilities). We also consider the general case of random individual risktolerances and analyze the related games in a complete market setting. Thisrandomness makes the problem substantially more complex as it leads to ($N$ ora continuum of) auxiliary ''individual'' It\^{o}-diffusion markets. For allcases, we derive explicit or closed-form solutions for the equilibriumstochastic processes, the optimal state processes, and the values of the games.

$N$-player and Mean-field Games in It\^{o}-diffusion Markets with Competitive or Homophilous Interaction