Fuzzy formulation of auctions and optimal sequencing for multiple auctions

Current research on auctions is mainly based on the game theory. In the first part of this paper, we propose a fuzzy set based formulation of auctions. We define fuzzy sets to represent the seller and buyersʹ valuations, bid possibilities and win possibilities. Analyzing the properties of these fuzzy sets, we study fuzzy versions of discriminating and nondiscriminating bidding strategies for each bidder in a single-object auction by using Bellman and Zadehʹs concept of confluence of fuzzy decisions instead of the game theoretic Nash equilibrium. The monotonically decreasing membership function replaces of the corresponding distribution density function in Milgrom and Weberʹs auction theory. In the second part of the paper, we develop a soft computing approach to maximize the sellerʹs revenue in multiple-object auctions through the use of object sequencing. The proposed sequencing approach is based on "fuzzy rule quantification". Numerical experience shows the potential of the proposed approach for application in practical auctions.