  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.
