## 1 Introduction  
As the need for information and communication technologies (ICT) increases, the spectrum auction of international mobile telecommunications (IMT) becomes more significant. The spectrum auction is a common way of selling the rights of signal transmission within a specific band of an electromagnetic section to telecommunication service providers [1]. For decades, most countries, including Australia, Hong Kong, India, Indonesia, Malaysia, New Zealand, Singapore, and South Korea, have adopted the spectrum auction to allocate their IMT spectrum blocks to telecommunication service providers [2, 3, 4, 5, 6]. This is because the auction is recognized as a fair way to allocate the limited IMT spectrum blocks to the service providers. Its operation is transparent and open to all participants, so that the entire process can be audited and verified by a third-party organization [7]. Moreover, the auction is beneficial to the government and the public. Once the auction starts, it can only be stopped when the bidding has stopped. This implies that the government can receive an offer with the maximum value from a bidder (i.e., a service provider). If the auction is fairly designed under mutual agreement between all participants, the monetary benefit can be utilized to enhance the quality of public life [8]. Although the spectrum auction is a rare event, as bidders purchase the spectrum at a high cost and are granted the right to use it for 5 or 10 years, it is an important issue because the benefit of the spectrum auction can reduce the national tax and be used for the research and development budget in the ICT field. On the other hand, the outcomes of the auction can be unsatisfactory. An auction is inappropriate for certain public spectrum blocks, such as emergency service and defense, which require protection and cyber security from harmful interference [9]. Considering that those public spectrum blocks are operated by tax, it is challenging to both increase the price of public spectrum use and reserve a wide range of spectrum blocks [8]. Moreover, according to auction styles, it is possible to have side effects that include bid sniping and an exposure problem (see Section 2.1 for more detail). Under the intensively competitive environment between bidders, it is possible that the contract price is far too high. In the spectrum auction of 700 MHz in 2008 in the U.S., the auction revenue was $19,592 million, which was much higher than the $7 billion expected by analysts [10]. To avoid potential problems, there are many studies of the methodologies of the spectrum auction, and the major methodologies are addressed in Section 2.1. Recently, a combinatorial clock auction (CCA) has been considered the best approach to avoid problems, such as bid sniping, as well as an exposure problem [11]. It is for this reason that South Korea adopted the clock auction (CA) with an ascending rule in 2018. In addition to the aforementioned, studies have been mainly conducted on how to design a fair auction for the recent issue of allocating 6G spectrum as well as 5G. For example, a method for designing dynamic spectrum sharing for 6G to accommodate the needs of various users was proposed by designing the auction process using game theory [12]. For an effective 5G auction in France, the partially observable Markov decision process (POMDP) was utilized to avoid solutions of a dynamic programming equation in the space of beliefs [13]. A quality of service (QoS)-aware priority-based spectrum management scheme [14] was devised to allocate spectrums in 5G and 6G to vertical sector players (VSPs) using a modified Vickrey-Clarke-Groves (VCG) auction mechanism to ensure minimum required bit rates for VSPs. Although these studies have been conducted with various methodologies to maximize the effectiveness of spectrum auctions, simulation-based decision-making methodologies have not yet been considered.