Impact of meta-order in the Minority Game

TL;DR

This paper investigates how a large, fixed trade affects market prices within the Minority Game framework, revealing that impact varies with market efficiency and providing exact analytical results.

Contribution

It introduces a detailed analysis of market impact in the Minority Game, linking information efficiency to trading costs and deriving exact impact measures using statistical mechanics.

Findings

Permanent impact is zero in the unpredictable phase.

Impact grows linearly with meta-order size in the predictable phase.

Exact characterization of market response in the predictable phase.

Abstract

We study the market impact of a meta-order in the framework of the Minority Game. This amounts to studying the response of the market when introducing a trader who buys or sells a fixed amount h for a finite time T. This perturbation introduces statistical arbitrages that traders exploit by adapting their trading strategies. The market impact depends on the nature of the stationary state: We find that the permanent impact is zero in the unpredictable (information efficient) phase, while in the predictable phase it is non-zero and grows linearly with the size of the meta-order. This establishes a quantitative link between information efficiency and trading efficiency (i.e. market impact). By using statistical mechanics methods for disordered systems, we are able to fully characterize the response in the predictable phase, to relate execution cost to response functions and obtain exact results for the permanent impact.