Equilibrium pricing of securities in the co-presence of cooperative and non-cooperative populations

TL;DR

This paper models equilibrium security prices in markets with both cooperative and non-cooperative agents, showing existence and convergence of equilibrium under certain conditions, especially when cooperative agents are few.

Contribution

It introduces a mean-field control framework for markets with mixed agent types and proves existence, uniqueness, and convergence of equilibrium prices.

Findings

Existence of a unique equilibrium when cooperative population is small.

Strong convergence of finite-agent models to the mean-field limit.

Development of a conditional extended mean-field control model.

Abstract

In this work, we develop an equilibrium model for price formation of securities in a market composed of two populations of different types: the first one consists of cooperative agents, while the other one consists of non-cooperative agents. The trading of every cooperative member is assumed to be coordinated by a central planner. In the large population limit, the problem for the central planner is shown to be a conditional extended mean-field control. In addition to the convexity assumptions, if the relative size of the cooperative population is small enough, then we are able to show the existence of a unique equilibrium for both the finite-agent and the mean-field models. The strong convergence to the mean-field model is also proved under the same conditions.