Mean-Field Price Formation on Trees with a Network of Relative Performance Concerns

TL;DR

This paper models how relative performance concerns among financial agents influence endogenous asset price formation in a mean-field equilibrium framework, using a binomial tree approach to establish existence, uniqueness, and numerical insights.

Contribution

It introduces a novel mean-field equilibrium model incorporating relative performance concerns with endogenous price determination in a binomial framework.

Findings

Existence and uniqueness of market-clearing mean-field equilibrium.

Numerical examples illustrating price distributions and agent behaviors.

Abstract

Financial firms and institutional investors are routinely evaluated based on their performance relative to their peers. These relative performance concerns significantly influence risk-taking behavior and market dynamics. While the literature studying Nash equilibrium under such relative performance competitions is extensive, its effect on asset price formation remains largely unexplored. This paper investigates mean-field equilibrium price formation of a single risky stock in a discrete-time market where agents exhibit exponential utility and relative performance concerns. Unlike existing literature that typically treats asset prices as exogenous, we impose a market-clearing condition to determine the price dynamics endogenously within a relative performance equilibrium. Using a binomial tree framework, we establish the existence and uniqueness of the market-clearing mean-field equilibrium in both single- and multi-population settings. Finally, we provide illustrative numerical examples demonstrating the equilibrium price distributions and agents' optimal position sizes.