A generator function is a simple and fundamental rule to a complex system. The generator function leads through manifold interaction to a very intricate system with so many layers on top of the original rule, that it becomes incredible hard to discern it. The generator functions of our physical world for example could be the basic forces determining the interactions of atoms: gravity, coulomb force... With these simple rules an incredibly complex universe has been created.
For our current Game A civilization:
"All (human induced) existential and catastrophic risks are symptoms of two underlying generator functions:
Rivalrous (win-lose) games multiplied by exponential technology self terminate [...] Complicated systems subsuming their complex substrate, becoming increasingly fragile till collapse becomes immanent." This comes from a great article on Daniel Schmachtenberger's blog Solving The Generator Functions of Existential Risk.