Non-existence and inefficiency of equilibria with American options

We analyze two examples of economies with incomplete financial markets. In the first model we consider a stock and an American put option on the stock. Although there is only one commodity and asset payoffs therefore do not depend on spot prices, we derive robust non-existence of equilibria. In the second model we consider an economy where a stock is the only asset available for trade. We show that it is impossible to complete the market by introducing American put options and that equilibria are inefficient. This example is also robust.