# Two-sided competition with vertical differentiation

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## Abstract

This paper studies duopoly in which two-sided platforms compete in differentiated products in a two-sided market. *Direct* competition on *both* sides leads to results that depart from much of the current literature. Under some conditions the unique equilibrium in pure strategies can be computed. It features discounts on one side and muted differentiation as the cross-market externality intensifies competition. Less standard, that equilibrium fails to exist when the externality is too powerful (that side becomes too lucrative). A mixed-strategy equilibrium always exists and is characterized. These results are robust to variations in the extensive form. The model may find applications in the media, internet trading platforms, search engine competition, social media or even health insurance (HMO/PPO).

## Keywords

Two-sided market Vertical differentiation Industrial organization Platform competition## JEL Classification

C72 D43 D62 L13 L15## Notes

### Acknowledgments

I am most grateful to Jean-Charles Rochet for helpful conversations. Thank you to Luis Corchon and Bill Schworm for their comments, and to Carlos Pimienta, Suraj Prasad, Francesco Sobbrio and Luis Vasconcelos for patiently reading earlier versions.

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