## 1 Introduction  
The electromagnetic spectrum is a vital and limited resource that is essential for various communication technologies including radio, television, mobile phones, and satellite-based communications. As the demand for wireless communications continues to grow, the need for efficient allocation of spectrum bandwidth becomes increasingly critical. One of the primary methods for assigning rights globally is through auctions. All frequencies within the electromagnetic spectrum, ranging from low-frequency radio waves to ultra-high frequencies such as gamma rays, are included in the spectrum's scope [1]. For communication purposes, the most relevant bandwidth ranges from 3 kHz to 300 GHz. Different frequencies exhibit distinct properties: low-frequency waves can cover larger spatial areas and penetrate buildings and solid objects, while higher-frequency waves can transmit more data, albeit over shorter distances [2]. Auctions have become the primary method for allocating spectrum usage rights to mobile operators for the implementation of 3G, 4G, and 5G networks. This trend of employing market-based approaches for spectrum management is expected to persist in 6G, with the design of auctions becoming more complex due to the diverse spectrum bands (low, mid, and high) that will be used, as well as coverage requirements, spectrum trading, and other considerations [3]. Historically, spectrum allocation grants have been managed using various methodologies and auction formats. Some of the mechanisms used throughout history have sufferedfrom inefficiencies, biases, or underutilization of the allocated spectrum. As demand for wireless services continues to grow throughout the world, it is imperative to explore new approaches to maximize efficiency in spectrum allocation. These auctions are typically conducted by regulatory authorities, such as the Federal Communications Commission (FCC) in the United States, Ofcom in the United Kingdom, and the Agencia Nacional de Telecomunicacoes (Anatel) in Brazil. Several key steps are followed throughout the auction process:  
* Planning and Consulting: The authorities identify the spectrum bands to be auctioned and consult with interested parties to determine the auction format and rules. * The auction project allows the authority to choose from several formats, including Simultaneous Multiple-Round Auctions (SMRAs), Combinatorial Clock Auctions (CCAs), Sealed Bid Auctions, and others. Each format has its own strengths and weaknesses, which the auctioneer must evaluate to achieve the specific goals of the auction process. * Concession and Payment: Once the dispute has been resolved, the successful bidders are awarded spectrum-specific licenses and are required to make payments to the authorities. The revenue generated from these auctions can be substantial, with some processes yielding billions of dollars. * Auctions within a spectrum context can lead several advantageous outcomes. * Efficient Allocation: The auction process facilitates the efficient allocation of spectrum to those participants who value it the most, as indicated by their bids, thereby promoting the optimal use of this resource. * Revenue: Governments, through regulatory agencies, can generate substantial revenue that can subsequently be utilized to fund public services, alleviate deficits, or reduce debt. * Innovation and Competition: Auction processes can incentivize innovation and competition within the telecommunication resulting in improved services and lower prices for consumers. * Guarantees and Counterparts: Several key rules may be established during the auction, requiring bidders to provide counterparts if they win. These counterparts may include investments in infrastructure, coverage, availability, and others factors, all aimed at ensuring a desirable outcome and promoting transparency. Although generally beneficial, auctioners must take action to address the shortcomings of each structure.