Fuzzy formulation of auctions and optimal sequencing for multiple auctions

doi:10.1016/S0165-0114(03)00127-1

Fuzzy Sets and Systems

Volume 142, Issue 3, 16 March 2004, Pages 421-441

https://doi.org/10.1016/S0165-0114(03)00127-1 Get rights and content

Abstract

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 buyers’ 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 Zadeh's 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 Weber's auction theory. In the second part of the paper, we develop a soft computing approach to maximize the seller's 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.

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The differences in sequential auctions are related to the sequencing of heterogeneous goods in procurement auctions due to the different orders [15]. ( b) Information asymmetry [16,17]. It is extremely difficult for seller to obtain accurate relevant information (such as valuation distribution and other information data [18]) of bidders, especially under different strategies or different situations. (
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To examine the impact of important simulation inputs such as buyer behavior on total revenues generated by various sequencing strategies, we employ a multi-scenario modeling process akin to Rodger (2013). Additionally, the optimization component of our framework extends previous studies using computational methods (e.g., genetic algorithm) to analyze sequencing decisions in auction settings where information is fully shared (Fang & Wang, 2004; Fatima, Wooldridge, & Jennings, 2010; Lyk-Jensen & Chanel, 2007). Second, we build on and extend the recent empirical studies investigating the effect of product sequencing decisions on seller revenue (Goes, Karuga, & Tripathi, 2010; 2012; Grether & Plott, 2009).
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^☆: This research was supported, in part, by the National Textile Center of the United States of America (Grant Number: I98S-01), and the National Natural Science Foundation (No. 60084003, 70171056) of the People's Republic of China.

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Fuzzy formulation of auctions and optimal sequencing for multiple auctions☆

Abstract

Fuzzy Sets and Systems

European Econom. Rev.

Fuzzy Sets and Systems

Artif. Intell.

Inform. Process. Lett.

Fuzzy Sets and Systems

Decision Support Systems

Decision Support Systems

Decision Support Systems

Information and Control

Cooperative fuzzy games

Math. Oper. Res.

Decision-making in a fuzzy environment

Management Sci.

Fuzzy convexity and peripheral core of an exchange economy represented as a fuzzy game

Fuzzy matrix games considering the criteria of the players

Kybernetes

Possibility Theory: An Approach to Computerized Processing of Uncertainty

Fuzzy Mathematics and Optimization