I'd hate to distill it down to something like Ayn Rand's ideas which ultimately smack of that counterfeit nihilism more properly called fatalist. The notorious live for today flower child mantra is just a restatement of the same.
Still, the practice of civilized ruthless selfishness, whether aggressive or passive, remains a variation of tooth and nail. Social Darwinism is the result, but that type of selection isn't what brought us this far as a species. It was natural selection that benefitted us across the ages.
But no political philosophy would deliver us into a way of life red in fang and claw. All of them are versions of civilizing, pushing us into a sort of collective refuge, to our detriment according to various sources, from natural selection itself.
So it would seem that an anti-political philosophy would be in order, but I believe even that would miss the essentials of nihilism and therefore couldn't be derived from it. I could be wrong, but in effect, you just can't get political theory from nihilism as it has been described for us.
Nihilistic reply intended