That is a paper by Paul Belleflamme and Eric Toulemonde, from a few years ago:
We analyze the effects of various taxes on competing two-sided platforms. First, we consider nondiscriminating taxes. We show that specific taxes are entirely passed to the agents on the side on which they are levied; other agents and platforms are left unaffected. Transaction taxes hurt agents on both sides and benefit platforms. Ad valorem taxes are the only tax instrument that allows the tax authority to capture part of the platforms’ profits. Second, regarding asymmetric taxes, we show that agents on the untaxed side benefit from the tax. At least one platform, possibly the taxed one, benefits from the tax.
This may all turn out to matter more if the new multinational corporate tax regime comes into existence. Of course you can vary the assumptions further yet, and get additional and differing results, but please keep in mind: the tax you impose is not the incidence you get.