The Combinatorial Multi-Round Ascending Auction

The Combinatorial Multi-Round Ascending Auction (CMRA) is a new auction format used in recent European spectrum auctions. We show that an auction-specific version of truthful bidding leads to an efficient allocation. We then characterize different ex post equilibria that feature truthful bidding, demand expansion, and demand reduction. The truth-telling equilibrium is fragile to small asymmetries in the bidders' caps. Moreover, if bidders are sufficiently symmetric, the CMRA is vulnerable to risk-free collusion. We propose an alternative activity rule that prevents such collusive strategies while keeping other equilibria intact. We discuss outcomes of several Danish CMRAs in light of our equilibrium predictions. (JEL D44, H82, L82)