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Auction models with lognormally-distributed multiplicative errors are used extensively in models of mineral lease sales. Equilibrium strategies are typically diﬀicult to calculate; multiplicative strategies are often used as approximations. An example based on a federal oﬀshore oil lease sale shows that multiplicative strategies may be quite far from being in equilibrium. However, under a special form of repetition, such strategies converge very rapidly to an equilibrium. The eﬀects of any ﬁxed costs, the reservation price, the number of bidders and the variance of the error are examined briefly for this example.
Engelbrecht-Wiggans, Richard, "Bidding in Auctions with Multiplicative Lognormal Errors: An Example" (1978). Cowles Foundation Discussion Papers. 735.