Implications of a Reserve Price in an Agent-Based Common-Value Auction

Abstract

Auction sellers can use a reserve price to require a minimum bid before items are sold. Theoretical and experimental research has tested the influence of a reserve price in an independent private values auction, but little focus has been given to the influence of a reserve price in a first-price common-value auction. We establish an agent-based first-price common-value auction to determine the impact of the reserve price with two buyers and with three buyers. An agent-based approach to this problem is both a unique contribution to the literature and appropriate since finding analytical solutions with common-value auctions is difficult. The agent-based model approach also allows us to consider buyers that have non-symmetric bid functions. Furthermore, we introduce a combination of numerical integration techniques with a new particle swarm learning algorithm. The buyers in the model choose their expected-net-revenue-maximizing bid price, and sellers choose their expected-revenue-maximizing reserve price. In the two-buyer and three-buyer auction, a reserve price increases the equilibrium winning bid price, decreases the probability that the item is sold, and increases the seller's expected revenue. A reserve price in a two-buyer auction increases the winning bid price more than including an additional buyer in the auction with no reserve price. However, due to only receiving a salvage value when the item does not sell in the auction, the seller's expected revenue is higher in the three-buyer first-price common-value auction without a reserve price than in the two-buyer auction with a reserve price.