There are many examples of markets involving two groups of agents who need to interact via 'platforms', and where one group's benefit from joining a platform depends on the number of agents from the other group who join the same platform. This paper presents theoretical models for three variants of such markets: a monopoly platform; a model of competing platforms where each agent must choose to join a single platform; and a model of 'competing bottlenecks', where one group wishes to join all platforms. The main determinants of equilibrium prices are (i) the relative sizes of the cross-group externalities, (ii) whether fees are levied on a lump-sum or per-transaction basis, and (iii) whether a group joins just one platform or joins all platforms.
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