VCG -Combinatorial Vickrey-Clarke-Groves Auctions

 Title: VCG - Combinatorial Vickrey-Clarke-Groves Auctions Authors: Marco B. Caminati, Manfred Kerber, Christoph Lange (math /dot/ semantic /dot/ web /at/ gmail /dot/ com) and Colin Rowat (c /dot/ rowat /at/ bham /dot/ ac /dot/ uk) Submission date: 2015-04-30 Abstract: A VCG auction (named after their inventors Vickrey, Clarke, and Groves) is a generalization of the single-good, second price Vickrey auction to the case of a combinatorial auction (multiple goods, from which any participant can bid on each possible combination). We formalize in this entry VCG auctions, including tie-breaking and prove that the functions for the allocation and the price determination are well-defined. Furthermore we show that the allocation function allocates goods only to participants, only goods in the auction are allocated, and no good is allocated twice. We also show that the price function is non-negative. These properties also hold for the automatically extracted Scala code. BibTeX: @article{Vickrey_Clarke_Groves-AFP, author = {Marco B. Caminati and Manfred Kerber and Christoph Lange and Colin Rowat}, title = {VCG - Combinatorial Vickrey-Clarke-Groves Auctions}, journal = {Archive of Formal Proofs}, month = apr, year = 2015, note = {\url{https://isa-afp.org/entries/Vickrey_Clarke_Groves.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License Status: [ok] This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.