## 3 Spectrum Auction Structures
### Combinatorial Clock Auction  
The Simultaneous Multiple-Round Auction was rapidly adopted worldwide, demonstrating significant improvements over its predecessors. However, over time, it became apparent that the auction format lacked a mechanism for players to understand each other's preferences and valuations. This deficiency led to protracted disputes, as each player attempted to \"feel\" the others' preferences by analyzing their previous bids, which were often minimal increments due to concerns about exposure.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Licenses**} \\
**Player** & **A** & **B** & **CD** & **ABCD** \\ \hline
1 & - & \(\epsilon_{1}\) & - & 20 \\
2 & 12 & \(\epsilon_{2}\) & - & - \\
3 & - & \(\epsilon_{3}\) & 10 & - \\ \hline \hline \end{tabular}
\end{table}
Table 6: AUSM.  
This mechanism, known as price discovery, became the primary focus of the next significant advancement in auction theory: the Combinatorial Clock Auction (CCA).  
The CCA structure consists of three distinct steps: the first two involve bidding and acceptance, while the third step focuses on the effective allocation of goods to the winners.  
The first stage involves the clock mechanism. In each round, the auctioneer announces a price for the goods being auctioned, and players submit the quantities they are willing to purchase at that price. If demand exceeds supply, a new round begins with \(p^{2}>p^{1}\). Players continue to submit their desired quantities until \(p^{*}\) is reached, where supply equals demand. This stage is designed to assist competitors in discovering their peers' pricing with minimal compromise.  
The second stage, as described by [18], consists of sealed offers for the goods. The players can bid for higher values or quantities than those stated in the first stage. The only restriction is that players must adhere to the Generalized Axiom of Revealed Preferences; that is, no player can offer less than what was revealed in the first stage of the auction, while also being bound by an upper limit, as illustrated in Figure 1.  
Bids revealed in the first stage of the auction are still regarded as active bids, while bids in the second stage are complementary and also considered active.  
According to [19], there are instances in which players can engage in detrimental actions by increasing prices or quantities, indicating that further investigation is necessary to address these behaviors.  
The auctioneer assesses all submitted bids from each round, in both stages, determining which resource allocation is most advantageous for all parties, while considering player eligibility.  
All bids are treated as all-or-nothing; that is, there is no possibility of arbitrary division within bid blocks. The price paid by each player is determined through the analysis of counterfactual scenarios to derive the Vickrey price. This mechanism encourages players to disclose their \(V_{i}\), bidding honestly, similar to a standard second-price auction.  
Figure 1: Generalized Axiom of Revealed Preference (GARP).  
The third and final stage of the CCA is known as the assignment phase. This stage is introduced to streamline the viable strategies identified in the first and second stages. The central idea is to consider goods as homogeneous whenever possible. For instance, the block 710-715 MHz is equivalent to the block 720-725 MHz.  
In a European auction [20], participants had the opportunity to bid on six homogeneous licenses within the 800 MHz spectrum block. During the first two phases, the items were considered identical, with their characteristics disclosed only in the third phase to speed up the process.  
Figure 2 was adapted from a presentation to the FCC by [PERSON] and [PERSON] in February 2013. It illustrates the Combinatorial Clock Auction. Notably, the first CCA occurred the following year.