{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T21:49:53Z","timestamp":1773352193939,"version":"3.50.1"},"reference-count":15,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","funder":[{"DOI":"10.13039\/501100001809","name":"National Nature Science Foundation of China","doi-asserted-by":"crossref","award":["11871366"],"award-info":[{"award-number":["11871366"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Research Innovation Program for College Graduate Students of Jiangsu Province","award":["KYCX21-2998"],"award-info":[{"award-number":["KYCX21-2998"]}]},{"name":"Research Innovation Program for College Graduate Students of Jiangsu Province","award":["KYCX20-2790"],"award-info":[{"award-number":["KYCX20-2790"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asia Pac. J. Oper. Res."],"published-print":{"date-parts":[[2023,2]]},"abstract":"<jats:p> Cloud\/ fog computing resource pricing is a new paradigm in the blockchain mining scheme, as the participants would like to purchase the cloud\/ fog computing resource to speed up their mining processes. In this paper, we propose a novel two-stage game to study the optimal price-based cloud\/ fog computing resource management, in which the cloud\/fog computing resource provider (CFP) is the leader, setting the resource price in Stage I, and the mining pools act as the followers to decide their demands of the resource in Stage II. Since mining pools are bounded rational in practice, we model the dynamic interactions among them by an evolutionary game in Stage II, in which each pool pursues its evolutionary stable demand based on the observed price, through continuous learning and adjustments. Backward induction method is applied to analyze the sub-game equilibrium in each stage. Specifically in Stage II, we first build a general study framework for the evolutionary game model, and then provide a detailed theoretical analysis for a two-pool case to characterize the conditions for the existence of different evolutionary stable solutions. Referring to the real world, we conduct a series of numerical experiments, whose results validate our theoretical findings for the case of two mining pools. Additionally, the impacts from the size of mining block, the unit transaction fee and the price of token on the decision makings of participants are also discussed. <\/jats:p>","DOI":"10.1142\/s0217595922400012","type":"journal-article","created":{"date-parts":[[2021,11,22]],"date-time":"2021-11-22T15:17:01Z","timestamp":1637594221000},"source":"Crossref","is-referenced-by-count":5,"title":["A Novel Two-Stage Game Model for Pricing Cloud\/ Fog Computing Resource in Blockchain Systems"],"prefix":"10.1142","volume":"40","author":[{"given":"Jinmian","family":"Chen","sequence":"first","affiliation":[{"name":"School of Business, Suzhou University of Science and Technology, Suzhou 215009, P. R. China"}]},{"given":"Yukun","family":"Cheng","sequence":"additional","affiliation":[{"name":"School of Business, Suzhou University of Science and Technology, Suzhou 215009, P. R. China"}]},{"given":"Zhiqi","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Business, Suzhou University of Science and Technology, Suzhou 215009, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2021,11,20]]},"reference":[{"key":"S0217595922400012BIB001","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/j.future.2020.02.045","volume":"108","author":"Chen Y","year":"2020","journal-title":"Future Generation Computer Systems"},{"key":"S0217595922400012BIB003","doi-asserted-by":"crossref","first-page":"153134","DOI":"10.1016\/j.aeue.2020.153134","volume":"118","author":"Cui Y","year":"2020","journal-title":"International Journal of Electronics and Communications"},{"issue":"1","key":"S0217595922400012BIB004","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1007\/s001910050054","volume":"8","author":"Friedman D","year":"1998","journal-title":"Journal of Evolutionary Economics"},{"key":"S0217595922400012BIB005","first-page":"281","volume-title":"International Conference on the Theory and Applications of Cryptographic Techniques","author":"Garay J","year":"2015"},{"issue":"13","key":"S0217595922400012BIB006","first-page":"53","volume":"1","author":"Houy N","year":"2016","journal-title":"Lcloud\/fogr Journal"},{"key":"S0217595922400012BIB007","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.comcom.2020.11.001","volume":"165","author":"Huang X","year":"2021","journal-title":"Computer Communications"},{"issue":"9","key":"S0217595922400012BIB008","doi-asserted-by":"crossref","first-page":"1975","DOI":"10.1109\/TPDS.2019.2900238","volume":"30","author":"Jiao Y","year":"2019","journal-title":"IEEE Transactions on Parallel and Distributed Systems"},{"key":"S0217595922400012BIB009","first-page":"1","volume-title":"2018 IEEE International Conference on Communications (ICC)","author":"Jiao Y","year":"2018"},{"issue":"3","key":"S0217595922400012BIB010","doi-asserted-by":"crossref","first-page":"420","DOI":"10.1109\/LWC.2017.2780128","volume":"7","author":"Liu M","year":"2018","journal-title":"IEEE Wireless Communications Letters"},{"key":"S0217595922400012BIB011","first-page":"1","volume-title":"2018 IEEE International Conference on Communications (ICC)","author":"Luong N","year":"2018"},{"key":"S0217595922400012BIB012","volume-title":"Bitcoin and Cryptocurrency Technologies: A Comprehensive Introduction","author":"Narayuan A","year":"2016"},{"issue":"3","key":"S0217595922400012BIB013","doi-asserted-by":"crossref","first-page":"2084","DOI":"10.1109\/COMST.2016.2535718","volume":"18","author":"Tschorsch F","year":"2016","journal-title":"IEEE Communications Surveys and Tutorials"},{"issue":"3","key":"S0217595922400012BIB014","doi-asserted-by":"crossref","first-page":"300","DOI":"10.1109\/LWC.2016.2547395","volume":"5","author":"Wang J","year":"2016","journal-title":"IEEE Wireless Communications Letters"},{"key":"S0217595922400012BIB015","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/j.cie.2019.05.005","volume":"133","author":"Wang T","year":"2019","journal-title":"Computers & Industrial Engineering"},{"issue":"3","key":"S0217595922400012BIB016","doi-asserted-by":"crossref","first-page":"4585","DOI":"10.1109\/JIOT.2018.2871706","volume":"6","author":"Xiong Z","year":"2018","journal-title":"IEEE Internet of Things Journal"}],"container-title":["Asia-Pacific Journal of Operational Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0217595922400012","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,16]],"date-time":"2023-03-16T05:53:57Z","timestamp":1678946037000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0217595922400012"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,20]]},"references-count":15,"journal-issue":{"issue":"01","published-print":{"date-parts":[[2023,2]]}},"alternative-id":["10.1142\/S0217595922400012"],"URL":"https:\/\/doi.org\/10.1142\/s0217595922400012","relation":{},"ISSN":["0217-5959","1793-7019"],"issn-type":[{"value":"0217-5959","type":"print"},{"value":"1793-7019","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,11,20]]},"article-number":"2240001"}}