We study the structure of markets when traders are given the opportunity to create their own market, as on the internet. On the Internet public exchanges have often been replaced by private exchanges. In our experiments, participants typically inform all traders on the other side of the market, but not on their own side, resulting in a private, not a public exchange. Even when we provide incentives for traders to inform each other, most of them reveal a strict preference to hide offers from rivals. Furthermore, with transaction costs these endogenously emerging private exchanges might lead to inefficiencies.