Abstract
Determining the winners in combinatorial auctions to maximize the auctioneer's revenue is an NP-complete problem. Computing an optimal solution requires huge computation time in some instances. In this paper, we apply three concepts of the game theory to design an approximation algorithm: the stability of the Nash equilibrium, the self-learning of the evolutionary game, and the mistake making of the trembling hand assumption. According to our simulation results, the proposed algorithm produces near-optimal solutions in terms of the auctioneer's revenue. Moreover, reasonable computation time is another advantage of applying the proposed algorithm to the real-world services.
Highlights
The combinatorial auctions support the complementarity for bidding
According to our simulation results, our proposed algorithm achieves 97.81% revenue comparing to the optimal solutions
Based on the above principle of searching the NE, we propose the Nash equilibrium search approach (NESA) to compute the winner set in the winner determination problem (WDP)
Summary
The combinatorial auctions support the complementarity for bidding. The complementarity means that bidders can bid several goods with a price. The combinatorial auctions are useful in the instances with some considerations. The Federal Communications Commission (FCC) used the combinatorial auction to sell electromagnetic spectra. Most bidders in the auction prefer to buy successive, rather than nonsuccessive, electromagnetic spectra. If the FCC used traditional auctions in selling a group of spectra to a single buyer, for example, the English auctions, the bidders may win some nonsuccessive spectra. After the FCC used the combinatorial auction to sell the electromagnetic spectra, the combinatorial auctions are widely applied to solve the optimization problems, such as the study of economic performance [2] and task assignment [3]
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