{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T06:25:58Z","timestamp":1777962358643,"version":"3.51.4"},"reference-count":14,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2021,5,4]],"date-time":"2021-05-04T00:00:00Z","timestamp":1620086400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Recently, owing to the trend of cross-disciplinary research in various fields, it is imperative to optimize the resource-allocation performance by analyzing allocation behavior and strategies from different perspectives as well as based on ideas from various fields. There are many decisive roles, such as changes in allocation behavior, related allocation methods, and the interaction and work effectiveness of strategies, to be implemented. By using game-theory analysis under resource-allocation procedures, in this article, we analyzed, constructed, simulated, and derived an efficient resource-allocation mechanism. Additionally, we generalized a power index by evaluating the operators and their activity levels. This article adopted the axioms of level completeness, criterion for weighted circumstances property, level synchronization, pure excess equal symmetry, and specific consonance to offer characterizations to assess the related rationality and accuracy of the proposed power index. Based on the above discussion, different from the rule of thumb, expert meeting, or other existing concepts, in this research game theory is used to provide an alternative guide for resource-allocation procedures by the optimal or equilibrium state established.<\/jats:p>","DOI":"10.3390\/sym13050799","type":"journal-article","created":{"date-parts":[[2021,5,5]],"date-time":"2021-05-05T22:51:42Z","timestamp":1620255102000},"page":"799","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Resource-Allocation Mechanism: Game-Theory Analysis"],"prefix":"10.3390","volume":"13","author":[{"given":"Shu-Lin","family":"Chang","sequence":"first","affiliation":[{"name":"Department of Early Childhood Education, Nanhua University, Chiayi 600, Taiwan"}]},{"given":"Kun-Chang","family":"Lee","sequence":"additional","affiliation":[{"name":"General Education Center, Chung-Jen Junior College of Nursing, Health Sciences and Management, Chiayi 600, Taiwan"}]},{"given":"Ruey-Rong","family":"Huang","sequence":"additional","affiliation":[{"name":"General Education Center, Chung-Jen Junior College of Nursing, Health Sciences and Management, Chiayi 600, Taiwan"}]},{"given":"Yu-Hsien","family":"Liao","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, National Pingtung University, Pingtung 900, Taiwan"}]}],"member":"1968","published-online":{"date-parts":[[2021,5,4]]},"reference":[{"key":"ref_1","unstructured":"Kuhn, H.W., and Tucker, A.W. 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Res."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"644","DOI":"10.1016\/j.fss.2008.10.003","article-title":"The consistent value of fuzzy games","volume":"160","author":"Hwang","year":"2009","journal-title":"Fuzzy Sets Syst."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/5\/799\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:57:00Z","timestamp":1760162220000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/5\/799"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,4]]},"references-count":14,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2021,5]]}},"alternative-id":["sym13050799"],"URL":"https:\/\/doi.org\/10.3390\/sym13050799","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,5,4]]}}}