Before revision:  The first one comprises the case where there is no hierarchy among players, and there is a symmetry of information. In this setting, we obtain closed-form formulas to the Nash equilibrium in the most general setting, i.e., when players' preferences are completely heterogeneous. Particularizing to the case of homogeneous parameters, we show that the average optimal inventory of the finite population converges to its mean-field counterpart, uniformly over a fixed trading horizon , as the population size grows to infinity .
After revision:  The first part of the work is where we examine the unconstrained problem, in which traders do not necessarily have to reach the end of the case of homogeneous parameters, we show that the average optimal inventory of the finite population converges to its mean-field counterpart, uniformly over a fixed trading horizon , as the population size grows to infinity .