## 2 Materials and Methods  
### Spectrum Auction  
As mentioned in the Introduction, the spectrum auction has become popular in many countries, including Australia, Hong Kong, India, Indonesia, Malaysia, New Zealand, Singapore, and South Korea, to sell the rights of providing telecommunication services via specific bands of the electromagnetic spectrum [2; 3; 4; 5; 6]. For example, Australia adopted the spectrum auction for IMT spectrum blocks involving 700 to 2600 MHz since 2013 [3]. Similarly, Hong Kong also utilized the auction system for wireless broadband in 2009 and 2011 [17]. The Ministry of Science and Information and Communications Technology (MSIT) in South Korea has sold IMT spectrum blocks involving 3.5 and 28 GHz since 2011 [18].  
There are four types of spectrum auctions, including the sealed bid auction, the simultaneous multiple round ascending auction (SMRA), the combinatorial clock auction (CCA), and the descending price combinatorial clock auction (DCCA). In a traditional sealed bid auction, all bidders submit their sealed bids to an auctioneer at the same time, and the highest bid is selected as the winner [19].  
The simultaneous ascending auction (SAA) was devised from the English auction that auctions multiple items in a single round, and the SAA repeats over multiple rounds in the SMRA [20]. Although the SMRA has been adopted more than 80 times since 1994 as a spectrum auction, there exists a major problem, known as bid sniping, in which a bidder waits until the end of each round and significantly increases either their bidding price or quantity [21]. Because this misbehavior disturbs the efficiency of the auction, the Federal Communications Commission (FCC) in the U.S. sets the regulation that, during an auction, each bidder should maintain a similar behavior tendency. In other words, a bidder cannot significantly increase their bidding price, as well as quantity [22]. Also, there exists the exposure problem that bidders reduce their bids to avoid losses caused from not winning all of the spectrum blocks [2].  
The CCA was devised to avoid problems associated with the SMRA by auctioning generic spectrum blocks. It consists of the clock phase expressing demand for the spectrum blocks, and one additional sealed-bid phase assigning a specific price and spectrum blocks to the bidders [11]. In this auction, the latest bid price is provided to all bidders like a \"clock\", and the generic spectrum is auctioned to bidders first. Because a bidder only bids for a quantity of spectrum, it is known as an appropriate approach when technologies used in a certain spectrum band are undecided [23]. The bidder can choose a technology after a specific spectrum band is allocated at the second stage [24]. In addition, similar to the CCA, the DCCA bids on packages of generic spectrum blocks, but it reduces bids over multiple iterations [25].  
Similar to the CCA, South Korea adopted the CA with an ascending rule for the IMT auction in 2018. This consisted of seven processes [26]: (1) collecting applications, (2) scheduling the auction, (3) conducting the auction, (4) allocating spectrum blocks, (5) payment, (6) cancellation, and (7) documentation. The IMT auction requires a big budget (e.g., the total price of the IMT auction for 28 generic blocks at 3.5 GHz in 2018 in South Korea was $3201.67 million), so that not all telecommunications companies can attend the auction. Thus, the government must understand the demand of the IMT market by collecting applications from major companies. Once there are multiple bidders, the government enables the auction schedule, conduct, and allocation. After the auction, all bidders have to pay their fee to the government. During the cancellation stage, a company that cannot pay the fee loses its right to use the IMT spectrum blocks, and then other companies are enabled to achieve the right to use the allocated IMT spectrum blocks for their business.