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.

翻译：组合式多轮递增拍卖（CMRA）是一种已在近期多个欧洲频谱拍卖中投入使用的新型拍卖机制。我们刻画了当竞拍者具有递减或非递减边际价值时，包含拍卖特有诚实报价、需求扩张和需求缩减形式的后验均衡。特别地，我们证明诚实报价均衡对竞拍者上限的微小不对称性具有脆弱性。另一方面，若竞拍者足够对称，CMRA易受无风险合谋的影响。我们提出一种替代性活动规则，该规则能阻止此类合谋策略，同时保持其余均衡不变。我们讨论了理论在多大程度上与丹麦频谱拍卖结果一致，以及如何利用竞拍数据检验我们的预测。