Abstract
We study a home rental market where hosts compete in prices and decide which guests to accept. Such screening results in inefficiently many rejections and can reduce welfare. In a unique symmetric equilibrium, hosts randomize over prices so that it may be unprofitable for them to accept some efficient trades. Moreover, every equilibrium is inefficient when there are few hosts. We further show that screening increases welfare when there are enough hosts or when the potential loss of surplus from inefficient trades is high. We discuss the implications of our findings to online platforms such as Airbnb and HomeAway.