How Minority Game Efficiency Shapes Meta-Order Market Impact

Summary

This study examines how a large trader’s finite period of steady buying or selling affects market impact in the Minority Game. The meta-order changes the market environment and creates statistical arbitrage opportunities, prompting other traders to adapt their strategies. The analysis connects the market’s information efficiency with the cost and persistence of executing a large order.

The reported result depends on the stationary phase of the model. In the unpredictable, information-efficient phase, permanent impact is zero; in the predictable phase, it is nonzero and increases linearly with meta-order size. The authors use statistical mechanics methods for disordered systems to characterize the predictable phase, connect execution cost to response functions, and derive exact permanent-impact results. These conclusions are theoretical results within the Minority Game framework; the description provides no empirical market validation or details about how directly the model’s phases map to live markets.

Key ideas

• A finite-duration meta-order perturbs the Minority Game and leads other traders to adapt.
• Permanent impact is reported as zero in the unpredictable phase.
• In the predictable phase, permanent impact is nonzero and grows linearly with order size.
• Statistical mechanics methods connect execution costs with market response functions.
• The stated findings come from a theoretical model, with no empirical validation described.

Tags

# Impact of meta-order in the Minority Game


# Impact of meta-order in the Minority Game









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.

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