Descending Price Multi-items Auctions

We propose a simultaneous descending price auction mechanism to sell multiple heterogeneous items to a number of buyers. Buyers have different known private valuation on each of the items, and each buyer wants at most one item. We show that if sellers follow a descending price offer procedure and the buyers follow a greedy strategy for accepting the offers, the auction mechanism results in a nearly efficient allocation with the final selling prices converging close to a competitive equilibrium price. The seller's descending price offer strategy is close to a Nash equilibrium. We also discuss the equilibrium strategy for the buyers. We show the buyers are better off waiting and there is a maximum limit (corresponding to the minimum competitive equilibrium price) till which they can wait without running into risk of loosing an item. Further, we prove that if the buyers wait within this limit, the prices can be brought arbitrarily close to a uniquely defined competitive equilibrium price.

Keywords: Competitive equilibrium; Dominant strategy; Dutch auction; English auction; Nash

JEL Classification Number: D44

By: Rahul Garg, Debasis Mishra

Published in: RI03008 in 2003


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