Descending price multi-item auctions

We propose a simultaneous descending price auction mechanism to sell multiple heterogeneous items, each owned by a distinct seller, to a number of buyers. Each buyer has known private valuations on items, and wants at most one item. We show that if the sellers follow a descending price offer procedure and the buyers follow a greedy strategy for accepting the offers, the auction results in a nearly efficient allocation, and terminates close to a competitive equilibrium price vector. The descending price offer strategy of the sellers is close to a Nash equilibrium. However, we show that the buyers are better off waiting in our auction. There is a maximum limit (corresponding to the minimum competitive equilibrium price vector) till which they can wait without running into the risk of not winning any item. If the buyers wait within this limit, the prices can be brought arbitrarily close to a uniquely defined competitive equilibrium price vector.