## 4 Theoretical Efficiency Comparison Between Combinatorial Auction Formats and Empirical Data  
In an article published in the _Proceedings of the National Academy of Sciences_, ref. [22] proposed a comparison of the SMRA structure (the primary format used by the FCC at that time), the round clock auction, and the Combinatorial Clock Auction. The authors proposed a comparison using a hypothetical auction of ten items to be sold as individual licenses. Several scenarios were imposed on the experiment to limit potential strategies, such as whether the licenses had synergies or were valid. Participants were incentivized to take the mock auctions seriously through monetary rewards based on their performance. Another observation was the magnitude of the effects, depending on whether the players possessed market power and the scenarios in which the effort required to displace the current winner was either higher or lower (gain). Figure 3 provides a comparison between CCA and SMRA. Table 7 compares 55 different auctions conducted by the authors, distinguishing each analyzed scenario. The authors concluded throughout the paper that the Combinatorial Clock Auction was superior to its peer in producing more efficient results, noting that it consistently achieved allocations close to 100%. Figure 2: CCA flowchart adapted from Ausubel and Baranov. Adapted from [21]. Since the spectrum is a limited resource, managing its allocation is essential. To this end, auctions have been widely adopted to promote efficiency. In many instances, revenue is not the primary determining factor; instead, considerations such as coverage, accessibility, infrastructure, and other aspects are important. In Economic Theory, each agent's interests can be represented through a utility function which all agents strive to maximize. However, revenue serves as a measurable indicator to assess the success of the auction, allocative efficiency, and participant interest. Two primary factors contribute to the value of a spectrum license: \((a)\) the band, measured in MHz, which is typically divided into blocks by regulatory authorities, and \((b)\) the population served by each license, as most cash flow projections rely on the expected revenue per user (ERPU). Consequently, a useful metric for comparing auction performance is the price/MHz/population (USD/MHz/pop). This metric aligns with analyses found in the international literature, such as [23]. Due to the heterogeneity of the observed auctions, we chose to consider the duration of each license in our study. To achieve this, we divided the USD/MHz/population by the length, in years, of the acquired exploitation rights. Data utilized consisted of auctions from North and South America between 2000 and 2024. These data are publicly accessible and generally available on each nation's official website. Figure 3: Auction format comparison: CCA vs. SMRA. Figure 4 illustrates the adoption trends by auction type. The rise of the Simultaneous Multiple-Round Auction (SMRA) during the first decade of the millennium can be attributed to its structure, which allows participants to bid on combinations of licenses. This feature is a critical factor in spectrum auctions, as it provides improved security for acquiring paired licenses. In 2014, the United States implemented its first CCA, which quickly became the dominant format in both the United States and Canada. It is also important to note that the