Equilibrium in the Presence of Many Insider Traders

The model has three kinds of traders: an insider, random noise traders, and a market maker. The insider aims to exploit her informational advantage and maximize expected profits while the market maker observes the total order flow and sets prices accordingly. The equilibrium of auction, when there are a noise trader, a insider trader and a price maker is well studied in the literature. However, in practice, there exist more than one insider and noise traders. In this paper, the case of κ insider traders are considered. First, the pure Nash equilibriums are derived and two learning methods namely gradient and partial best response are studied. Then, the effect existence of more than one insider traders in the market on equilibriums and learning methods are considered. Also, mixture equilibriums are derived and corresponding learning method for mixture distributions is derived. Finally, a conclusion is proposed.