Phase Transitions in Kyle's Model with Market Maker Profit Incentives

We consider a stochastic game between three types of players: an inside trader, noise traders and market maker. In similar fashion to Kyle's model, we assume that the insider first chooses size her market-order then maker determines price by observing total order-flow resulting from transactions. addition classical framework, revenue term is added maker's performance function, which proportional order flow bid-ask spread. derive maximizer for insider's function prove sufficient conditions equilibrium in game. Then, use neural networks methods verify this holds. show state model experience interesting phase transitions, as weight changes. Specifically, asset different phases: linear pricing rule without spread, includes mid-price metastable with zero large