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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 truthtelling 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.
