{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,23]],"date-time":"2025-12-23T10:02:08Z","timestamp":1766484128000,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2019,5,22]],"date-time":"2019-05-22T00:00:00Z","timestamp":1558483200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["Grant No. 2018M643683"],"award-info":[{"award-number":["Grant No. 2018M643683"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Ministry of Education and China Mobile Joint Research Fund Program","award":["Grant No. MCM20160302"],"award-info":[{"award-number":["Grant No. MCM20160302"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["Grant Nos. 91746111, 71702143, 71731009, 71732006"],"award-info":[{"award-number":["Grant Nos. 91746111, 71702143, 71731009, 71732006"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The Internet of Underwater Things (IoUT) is an evolving class of Internet of Things and it is considered the basic unit for the development of smart cities. To support the idea of IoUT, an Underwater Sensor Network (USN) has emerged as a potential technology that has attractive and updated applications for underwater environment monitoring. In such networks, route selection and cluster-head management are still challenging. As the optimal routes always lead to congestion and longer delays while the cluster-head mismanagement leads to ending the USN lifespan earlier. In this paper, we propose a cooperative clustering game that is based upon energy heterogeneity and a penalty mechanism to deal with the cluster head mismanagement issue. Then, we use a non-cooperative evolutionary game for the best relay selection; the results prove that this utility function is the most suitable solution for the relay selection and its strategy selection converges to Nash Equilibrium. The proposed framework is compared with recent schemes using different quality measures and we found that our proposed framework performs favorably against the existing schemes for all of the evaluation metrics.<\/jats:p>","DOI":"10.3390\/s19102351","type":"journal-article","created":{"date-parts":[[2019,5,23]],"date-time":"2019-05-23T03:22:03Z","timestamp":1558581723000},"page":"2351","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A Hybrid Energy Equating Game for Energy Management in the Internet of Underwater Things"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2911-1981","authenticated-orcid":false,"given":"Gulnaz","family":"Ahmed","sequence":"first","affiliation":[{"name":"School of Management, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xi","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Management, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mian Muhammad Sadiq","family":"Fareed","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,5,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1879","DOI":"10.1016\/j.jnca.2012.07.012","article-title":"An overview of the internet of underwater things","volume":"35","author":"Domingo","year":"2012","journal-title":"J. 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