On the Non-Existence of Multiplicative Equilibrium Bidding Strategies

Extensive use has been made of multiplicative bidding strategies in the literature relating to auctions of mineral leases. It is shown that, generally, multiplicative strategies are not in equilibrium. It is also established that an equilibrium bidding strategy is not a function merely of a sufficient statistic for the true value, or of any other of a class of related statistics, if an individual bidder observes more than one piece of information. The general insufficiency of a single simple statistic is briefly discussed and a special class of models is identified in which a single statistic is indeed strategically sufficient.