Lemons and peaches: Multi-stage buying mechanisms with a Devil’s Menu

We introduce a four-stage, multi-price buying mechanism which can be used by a (big) buyer to separate low-quality sellers – called “lemon” owners – from high-quality sellers – called “peach” owners. With a partition of sellers into several groups, the buyer obtains the commodities from a desired number of “peach” owners at a price that matches their willingness to sell. For their part, “lemon” owners are trapped into selling their items at a low, or even negligible, price. We discuss several variants of this mechanism – generically called a Devil’s Menu – and show how the degree of surplus extraction by the buyer is related to the number of prices used and to the extent to which items can be bought sequentially. The common feature of all the variants is that they allow the buyer to neglect those partition groups with the highest number of false claims made by sellers who own lemons. This, in turn, yields equilibria in which no false claims are made. Our results are robust for several extensions of our baseline setup. Finally, we offer applications of our insights for market regulators, political interest groups, and decoy ballots.