## 5 Conclusions  
This study has proposed a novel simulation modeling approach for the IMT spectrum auction design under ABS with three telecommunications service provider types (i.e., the Aggressive bidder, the Moderate bidder, and the Conservative bidder). Due to the high-value spectrum rights, it is significant to fairly allocate generic IMT spectrum blocks to existing service providers. To this end, most countries, such as the U.S., Germany, and South Korea, have adopted the IMT spectrum auction as the best way for spectrum block allocation. However, it is challenging to identify the minimum bidding price that can provide fair opportunities to all bidders. If a government agency sets unfair auction rules, it can intimidate liberalization of the IMT market. This should not be happening in countries that are committed to free competitive markets. To overcome the potential problem, the proposed approach has considered the three provider types and their competitiveness in the auction. The exponential utility theory and Vickrey-nearest core pricing theory have been adopted and devised for the realistic decision-making behavior modeling of the agents. The developed ABS was calibrated to the IMT spectrum auction conducted in 2018 in South Korea. Moreover, calibration and optimization models were developed for accurate modeling of the ABS. In particular, the best minimum pricing policy was identified by the meta-heuristic optimization provided by OptQuest\({}^{\text{\textregistered}}\). In the experiments, three cases with different minimum bidding prices (i.e., low price case, high price case,and the optimal price) were considered and analyzed. As a result, this study found that the minimum bidding price should be designed regarding the budget of the Conservative bidder to provide equal opportunities to all bidders. If the price only tried to maximize the final contract price, there is no reason to have the auction. In this case, only the company with a competitive advantage can buy the IMT spectrum blocks, so that a monopolistic market will appear. The proposed approach will help the government agency prevent this problem in advance. This study is the first to model the IMT spectrum auction process using agent-based simulation and simulation-based optimization and to suggest the optimal initial bidding price. However, this study has several limitations. First, the case is limited to the IMT spectrum auction in which three Korean companies participated. Although the proposed methodology can model cases with a variety of participants, additional research is needed to determine how appropriately the exponential utility theory and Vickrey-nearest core pricing theory used in the study can model decision-making behavior in the environments of other countries. In addition, the definitions of (1) the Aggressive bidder, (2) the Moderate bidder, and (3) the Conservative bidder need to be changed for each country, and the parameters of the proposed simulation model need to be re-calibrated. Finally, additional data needs to be secured to utilize the proposed methodology. However, since the IMT spectrum auction is not an annual event, but rather a very rare event, such as every 5 or 10 years, it is difficult to collect data for modeling. For future study, additional behavior data of bidders' decision-making should be collected. The data will help engineers design reliable and fair spectrum auctions involving the minimum bidding price, increment rate, and required number of bidding rounds. In addition, the proposed approach needs to be applied to multiple auction cases in different countries, so that it can be more generalized. Conceptualization, S.-Y.K. and S.K. ; methodology, S.-Y.K. and S.K. ; software, S.K. ; validation, S.-Y.K. and S.K. ; formal analysis, S.-Y.K. and S.K. ; investigation, S.-Y.K. and S.K. ; resources, S.-Y.K. ; data curation, S.K. ; writing--original draft preparation, S.-Y.K. and S.K. ; writing--review and editing, S.-Y.K. and S.K. ; visualization, S.K. ; supervision, S.-Y.K. ; project administration, S.-Y.K.