Simplifying Composite Functions

For real numbers $x$ and $y$, define $$\nabla(x,y)=x-\frac1y .$$ What is the value of $$\underbrace{\nabla(2, \nabla(2, \nabla(2, \ldots \nabla(2,\nabla(2, 2)) \ldots)))}_{2016 \,\nabla\text{s}}?$$ Express your answer as a fraction in lowest terms.

(Source: NIMO 23)