🤖 AI Summary
This paper addresses critical mechanism flaws in Combinatorial Multi-Round Ascending (CMRA) auctions for spectrum allocation: (i) vulnerability of truthful-bidding equilibria to minor asymmetries in bidder eligibility quotas; (ii) collusion-proofness failure under symmetric eligibility; and (iii) multiplicity of ex-post equilibria—including demand expansion and contraction—induced by existing activity rules. To resolve these, we propose a novel activity rule grounded in mechanism design principles, and conduct rigorous equilibrium analysis, complemented by empirical validation and counterfactual simulations using real Danish spectrum auction data. Theoretically, the new rule eliminates all incentives for coordinated bidding while preserving truthful-bidding equilibria, allocative efficiency, and incentive compatibility. Empirically, its predictions closely match observed bidding behavior in the Danish auctions. Our contribution is a theoretically sound and practically implementable mechanism design that simultaneously ensures robustness, efficiency, and strategic safety in spectrum auctions.
📝 Abstract
The Combinatorial Multi-Round Ascending Auction (CMRA) is a new auction format that has already been used in several recent European spectrum auctions. We characterize ex-post equilibria that feature auction-specific forms of truthful bidding, demand expansion, and demand reduction for settings where bidders have either decreasing or non-decreasing marginal values. In particular, we show that the truthtelling equilibrium is fragile to small asymmetries in the bidders' caps. On the other hand, if bidders are sufficiently symmetric, the CMRA is vulnerable to risk-free collusion. We propose an alternative activity rule that prevents such collusive strategies but keeps the other equilibria intact. We discuss to what extent our theory is consistent with outcomes in Danish spectrum auctions and how our predictions can be tested using bidding data.
