Penerapan Nilai Shapley untuk Menghitung Pembagian Keuntungan dalam Pelelangan
Mivo Ardiyantaka, Prof. Dr. Salmah, M.Si.
2024 | Skripsi | MATEMATIKA
Auction is a compelling method within the realm of buying and selling goods, as it involves a competitive process among buyers to submit purchase bids to secure the item being offered for sale. Auctions can be studied through a game theory approach by considering the auction as a game with players consisting of sellers and buyers. In an auction, there are payments to be made by the auction winner. The payment amount is calculated based on the winning bid and the surplus shares received by the auction winner. The surplus shares among players can be calculated using the Shapley value formula learned in n-players cooperative games. However, the standard Shapley value formula tends to allocate surplus to losing players, making it less suitable for calculating surplus shares in auctions.
This thesis will discuss how the Shapley value formula can be adjusted and applied to calculate surplus shares in auctions. The adjustment is made by dividing the set of players into a set of winning players and a set of losing players. Thus, the Shapley value formula is more appropriate as the basis for payment rules in auctions. A rule will be formed called the Balanced Winner Contribution rule (BWC rule) which satisfies the principle of fairness. Several examples are presented to illustrate how the BWC rule works. From the discussions in this thesis, it is concluded that the Shapley value formula can be adjusted and applied to calculate surplus shares in auctions while still maintaining compliance with the necessary axioms.
Kata Kunci : Teori Permainan, Nilai Shapley, Pelelangan, Lelang Vickrey, Pembagian Surplus