I don't think Either of them would really be able to do what they are doing without having at least some kind of assurance that the other's plans wont interfere. Otherwise I think both would consider the other too dangerous to live.
I tend to agree.
It helps that both see an opportunity in the chaos they both help create (and which each, on his own**, would find it hard, if not impossible, to produce). Oh, and each gives the other a suspect*** at whom to point if someone powerful finally realises that certain events are not as random as they may first seem, and all other candidates for being the cause can be shown to have been unable to conjure up the event(s) concerned.
** - And it allows each the opportunity to be able to truly demonstrate his lack of involvement in some aspects of the chaos: "I can prove that I had nothing to do with X, Y or Z," said Varys/Littlefinger, "and I can show how I was disadvantaged as a result of each of them. On the other hand, Littlefinger/Varys was around and did benefit." "I can prove that I had no involvement in A, B or C," said Littlefinger/Varys, "and I can show how I was put at a disadvantage as a result of each of them. Varys/Littlefinger, on the other hand, did gain by them, and had every opportunity to arrange them."
*** - This would, inevitably, be each's very last shot**** at attempting to clear himself, which is why each does his best to plausibly implicate others, either by showing how they might be involved (e.g. Tyrion and the knife that almost killed Bran, Sansa being on hand -- and carrying the poison -- with at least one motive for killing Joffrey), or getting them to do the dirty work (e.g. Lysa poisoning her husband, Olenna poisoning Joffrey).
**** - And each would want to make himself scarce (or have the other quickly and safely dispatched) before the other had an opportunity to return the favour. (Which, as someone pointed out above, gives each a reason not to implicate the other too soon, as it would be risking both their lives, and both their plans.)
