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The radio network controller is the first layer, the base stations are the second layer, and the base station users are the third layer. The stackelberg game model is used between the first and second layers, in which the radio network controller is the leader and the base stations are the followers. The radio network controller sets the interference prices for the base stations and the users in the third layer can update their transmission power by non-cooperative game based on the setting interference price. According to the proposed scheme, the users power allocation can reach the Nash equilibrium through by non-cooperative game and obtain the optimal transmission power. Moreover, it is proved that the equilibrium solution is composed of the optimal price and the optimal transmission power, and the convergence of this algorithm is also verified. The simulation results show that the proposed algorithm can decrease the interference and improve the system capacity.<\/jats:p>","DOI":"10.1186\/s13638-020-01866-3","type":"journal-article","created":{"date-parts":[[2020,12,1]],"date-time":"2020-12-01T08:04:14Z","timestamp":1606809854000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A hierarchical game-based power allocation algorithm in 5G heterogeneous integrated networks"],"prefix":"10.1186","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9432-0563","authenticated-orcid":false,"given":"Geng","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luyao","family":"Ma","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qingtian","family":"Zeng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinjin","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,12,1]]},"reference":[{"issue":"6","key":"1866_CR1","doi-asserted-by":"publisher","first-page":"1065","DOI":"10.1109\/JSAC.2014.2328098","volume":"32","author":"J Andrews","year":"2014","unstructured":"J. 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