  We examine dynamic coupling and feedback effects between High Frequency
Traders (HFTs) and how they can destabilize markets. We develop a general
framework for modelling dynamic interaction based on recurrence relations, and
use this to show how unexpected latency and feedback can trigger oscillatory
instability between HFT market makers with inventory constraints. Our analysis
suggests that the modelled instability is an unintentional emergent behaviour
of the market that does not depend on the complexity of HFT strategies - even
apparently stable strategies are vulnerable. Feedback instability can lead to
substantial movements in market prices such as price spikes and crashes.
