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The Combinatorial Multi-Round Auction (CMRA) is a new auction format whichhas already been used in several recent European spectrum auctions. Wecharacterize equilibria in the CMRA that feature auction-specific forms oftruthful bidding, demand expansion, and demand reduction for settings in whichbidders have either decreasing or non-decreasing marginal values. Inparticular, we establish sufficient conditions for riskless collusion. Overall,our results suggest that the CMRA might be an attractive auction design in thepresence of highly complementary goods on sale. We discuss to what extent ourtheory is consistent with outcomes data in Danish spectrum auctions and how ourpredictions can be tested using bidding data.

The Combinatorial Multi-Round Ascending Auction