Bilateral trading with naive traders

We introduce naive traders in bilateral trading. These traders report their true types in direct mechanisms and bid/ask their values/costs in auctions. We show that by expropriating naive traders in direct mechanisms, the mechanism designer can subsidize additional trades by strategic traders and improve efficiency ex-post compared to when both traders are surely strategic. In fact, complete expropriation of naive traders is a necessary condition for constrained efficiency. A significant implication is that in the presence of naive traders, ex-post individually rational mechanisms are not constrained efficient. In contrast, if the traders use fixed mechanisms, then efficiency can decrease when naive traders are introduced.