Auction bidding when the cost is rising

Prices in procurement auctions are frequently required to remain fixed for a certain time period of validity. If the underlying cost rises, as for example due to inflationary economic conditions or changes of the production input prices, the eventual profit when awarding takes place may be dramatically lower than anticipated. In response, the administration of a firm can impose a bidding constraint restricting the probability that profitability stays below a pre-determined target. In this setting, we derive the equilibrium bidding strategies when the cost changes with upward drift continuously in time. We determine the effect of the validity time to the expected bidder profit and show how bidders can profit if the uncertainty of cost is correctly managed. We demonstrate that the contracting authority always suffers from a prolonged validity time in terms of the expected project cost and we develop methods to determine the optimal validity time of the bids. We explore and compare mechanisms of dynamic pricing allowing adjustments of the bids which can partially or totally compensate against cost exposure. We conclude with a discussion of the findings and recommendations for both bidders and auctioneers on the appropriate management of the impact of rising cost.