Before revision:  In the second framework, we consider a major player, also called a leader, with the first move advantage, and a population of minor players, also known as followers, thought of as high-frequency traders, which trade on informational advantage against the leader. This leads to a model of McKean-Vlasov type for the dynamics of the asset's midprice.
After revision:  In the sequel, we proceed to analyze the constrained situation as an asymptotic limit of the previous one.