various settings, including different kinds of utilities, equilibrium pricing, and state constraints, but none incorporate consumption.

There are two natural arguments for studying relative consumption concerns. On the one hand, interpreting agents as fund managers, we may think of consumption as capital accumulation, in the form of equipment, technology, or benefits for employees. A high relative consumption in this sense would naturally attract clientele or better employees, and more generally it should lead to similar benefits as a high relative wealth. On the other hand, if we interpret the agents in our model as household investors, then relative consumption concerns fit naturally with models of *keeping up with the Joneses*; this line of literature directly incorporates the social aspects of investment and consumption decisions [@abel1990asset; @chan2002catching; @demarzo2004diversification; @gali1994keeping].

Our paper contributes to the literatures on optimal consumption and investment as well as the application of mean field games. The dynamic problem of lifetime consumption and investment planning with one player was formalized and studied in the landmark papers of Merton [@merton1969lifetime; @merton1975optimum] and Samuelson [@samuelson1975lifetime]. Later work incorporated more complex features into the models, such as general price processes, bankruptcy, etc. [@karatzas1987optimal; @karatzas2003optimal]. Those that incorporated *multiple agents* into the 