Search platforms: showrooming and price parity clauses

We provide a model in which consumers search for firms directly or through platforms. Platforms lower search costs but charge firms for the transactions they facilitate. Platform fees raise the possibility of showrooming, in which consumers search on a platform but then switch and buy directly to take advantage of lower direct prices. In settings like this, search platforms like Booking.com have adopted price parity clauses, requiring firms to offer their best prices on the platform, arguing this is needed to prevent showrooming. However, despite allowing for showrooming in our model, we find that price parity clauses often harm consumers.