Auction Design without Commitment

We study auction design when parties cannot commit themselves to the mechanism. The seller may change the rules of the game and the buyers choose their outside option at all stages. We assume that the seller has a leading role in equilibrium selection at any stage of the game. Stationary equilibria are characterized in the language of vonNeumann-Morgenstern stable sets. This simplifies the analysis remarkably. In the one buyer case, we obtain the Coase conjecture: the buyer obtains all the surplus and efficiency is reached. However, in the multiple buyer case the seller can achieve more: she is able to commit to the English auction. Typically the converse also holds, the English auction is the only stable auction mechanism.