Bidding Decisions with Nonequilibrium Strategic Thinking in Reverse Auctions

This paper considers decisions of bidders with bounded rationality in different thinking levels for a first-price sealed-bid reverse auction. To characterize the nonequilibrium strategic thinking, we construct a mathematical model that incorporates the “level-k decision rule” to iteratively derive closed-form solutions. Then the effects of bidders’ heterogeneous beliefs of thinking levels on their bid prices and expected payoffs are investigated. We find that under some assumptions, bidders will exhibit oscillating behavior in their bid prices and expected profits in terms of thinking levels. When the thinking level tends to infinity, the bid prices and expected profits converge to those in the conventional analysis with perfectly rational bidders. An interesting finding from theoretical analysis verified by numerical experiments is that any bidder with a thinking level above two should bid according to level-2 bidder’s strategy to achieve the highest expected profit, and in this case the buyer will pay no more than level-2 bidder’s bid price.