Combinatorial auction under fuzzy environment

Abstract

Combinatorial auction (CA) mechanism allows bundling of multiple items in packages, which can be solved through a clearing method termed as the winner determination problem (WDP). However, to date, there has yet to be a CA model that accounts for the fuzziness of bidders’ submitted prices. The imprecision in submitted prices is the result of the time gap between bid placement and winning bid announcement, which reflects the bidders’ expected values of the goods at the point of contract sale. Despite this common understanding, conventional CA modeling still treats the prices as deterministic. This causes a major shortcoming when an uncertain environment is assumed to be deterministic and solved through conventional WDP. This study shows that a fuzzy environment modeled via a deterministic WDP approach provides overly optimistic revenue for the auctioneer. A method of using possibilistic distributions of submitted prices to account for price uncertainty is proposed and formalized as Fuzzy Combinatorial Auction Winner Determination Problem (Fuzzy CA WDP). The difference in optimal solutions in deterministic WDP and fuzzy WDP reflects the amount of over estimation when a fuzzy situation is treated as though it is precise. It also reflects the information value when the uncertainty inherent in the fuzzy environment is resolved. Given that the information value is quantified in unit dollars, the fuzzy WDP approach allows the auctioneer to estimate its “true” revenue despite price uncertainties.