AGTA Tutorial 8
Please attempt the question before your tutorial.
1. Suppose you are running a VCG-based simultaneous multi-item auc- tion, where three related items A, B, and C, are being auctioned simultaneously, and each bidder can bid on any possible subset of the items. Suppose there are two bidders, X and Y , and they provide you with their “claimed valuation” as their bids for every subset of the items, as part of the bidding process. Suppose that the valuation functions vX and vY that you receive from the two bidders, X and Y, respectively, are as follows (the numbers denote millions of pounds):
vi(∅) vi(A) vi(B) vi(C)
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vi({A, B}) 29
vi({A, B, C}) 50
i:=X 0 24 4 9 i:=Y 0 15 18 11
vi({B, C}) 34 32
vi({A, C})
• What is the outcome of this VCG auction? In other words, which of the two bidders will get which of the item(s), and what price will they each pay?
• Do you expect the bidders to tell you the truth about their val- uations?
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