Maybe ... I'm more a picking the tool to fit the problem kind of economist, so I would say that in this case, that fact that the size of the other city in the pair is a main factor in determing the percentage market share leads one into the logarithmic family. Its a main reason why the ratio of populations between adjoining levels of the central place hierarchy tends to be close to constant (for most developed economies). And in the logarithmic family, the simplest mean is:

antilog( (log(x1)+log(x2))/2 )

which in direct arithmatic is:

(x1*x2)^.5

I've been accused of being a Marxist, yet while Harpo's my favourite, it's Groucho I'm always quoting. Odd, that.