VCG Mechanism (Vickrey-Clarke-Groves)
The VCG Mechanism (Vickrey-Clarke-Groves) is a mechanism used for funding public goods. It ensures Pareto Efficiency by allocating goods based on the participants' declared willingness to pay. Each participant can submit bids for multiple goods. For example, let's consider the case of coffee and cake. Participants can choose to buy either coffee or cake, or both.
1. Bidder1 bids $6 for coffee only.
2. Bidder2 bids $8 for the coffee and cake set.
3. Bidder3 bids $5 for cake only.
To achieve Pareto Optimality, it is efficient to sell the goods separately. Therefore, coffee is priced at $6 and cake at $5. However, there is a condition that the winner pays the minimum amount within the range that allows them to remain the winner (critical value). As a result, the actual purchase amounts may differ. You can refer to the following links for more information on the critical values:
- https://gyazo.com/f1048d0f2dada2b11551aaff8c52990e
- https://gyazo.com/b1692fa8bc99feab86b35e8a0be14458
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Additionally, the auction system, including Mechanism Design, VCG Mechanism, and Spectrum Auction, is utilized by companies like GAFA (Google, Apple, Facebook, Amazon) to generate huge profits. This system has even been recognized with the Nobel Prize in Economics.