Kauhanen, H. (2019) Stable variation in multidimensional competition. In A. Breitbarth, M. Bouzouita, L. Danckaert & M. Farasyn (eds.) *The Determinants of Diachronic Stability*, 263–290. Amsterdam: John Benjamins.

The Fundamental Theorem of Language Change (Yang, 2000) implies the impossibility of stable variation in the Variational Learning framework, but only in the special case where two, and not more, grammatical variants compete. Introducing the notion of an advantage matrix, I generalize Variational Learning to situations where the learner receives input generated by more than two grammars, and show that diachronically stable variation is an intrinsic feature of several types of such multiple-grammar systems. This invites experimentalists to take the possibility of stable variation seriously and identifies one possible place where to look for it: situations of complex language contact.