The same way game theory is used in regular trading- bartering. Basically, trading/HFT is a very simplistic form of bartering/exchange, right? What do you think?
HFT is just buying at a price a tiny fraction cheaper than someone else is prepared to buy for a near instantly selling it to them for a tiny fraction price improvement. Generally talking 1cent
I do not think game theory applies to hft. hft utilizes technology, knowledge of regulations and market microstructure to actively participate in the markets as intermediary between market players. The role of hft is purely technical and is practically a form of modern market making.