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

TL;DR

This paper extends Kyle's market model by adding a revenue-based incentive for the market maker, revealing phase transitions in equilibrium pricing strategies as the incentive varies, demonstrated through analytical and neural network methods.

Contribution

It introduces a modified Kyle's model with profit incentives, derives equilibrium conditions, and uncovers phase transitions in pricing strategies using neural networks.

Findings

Identification of three distinct equilibrium phases

Demonstration of phase transitions as revenue incentive varies

Validation of equilibrium states with neural network methods

Abstract

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