Collusion between bidders can lead to a loss in revenue and is a significant concern in practical auction design. For simplicity, we assume for this exercise that bidder values are known to all bidders.
1. Consider a SPSB auction. Suppose bidders with values 4, 8 and 10 collude, while a fourth bidder’s bid is fixed at $6. How can bidders 1, 2 and 3 bid in order to collude, how might their proceeds be divided to keep all members of the coalition happy, and why can bidders 1 and 2 not usefully deviate from this play? (You do not need to provide a formal equilibrium analysis.)
2. Now consider a FPSB auction for the same setting. Considering bids that bidders 1, 2 and 3 might place such that one of them wins for just above $6, does the FPSB auction seems more or less robust to collusion than the SPSB auction?
3. Shill bidding occurs when a bidder representing the auctioneer places a bid, trying to increase the payment from the winner. Explain why shill bidding is a problem in the SPSB auction, and how the equilibrium analysis of the auction would change.
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