360　video　applications　are　attracting　more　attention　in　broadcasting　systems.　In　the　case　of　limited　bandwidth,　the　bit　fluctuation　will　affect　the　perception　quality　when　transmitting　360-degree　videos.　To　further　optimize　the　bit　allocation　and　reduce　fluctuation,　this　paper　proposes　a　virtual-competitors-based　Rate　Control　(RC)　algorithm　for　360-degree　video　coding.　The　virtual　competitors＇　concept　is　first　proposed　to　balance　the　volatility　of　the　bit　between　the　adjacent　GOPs.　In　addition,　by　introducing　game　theory,　the　virtual　competitors-based　frame-level　bit　allocation　model　is　instructed.　Furthermore,　we　propose　a　GOP-level　bit　allocation　scheme　with　the　average　encoded　bits　of　the　historical　GOP,　the　remaining　bits　of　the　encoded　video　sequence,　and　the　number　of　unencoded　GOPs.　Based　on　the　designed　frame-level　and　GOP-level　bit　allocation　scheme,　the　overall　bit　allocation　method　is　proposed　to　implement　the　lower　GOP-level　bit　fluctuation.　Experimental　results　indicate　the　proposed　method　with　the　optimal　RC　Error,　Bjontegaard　Delta　Peak-Signal-to-Noise-Ratio,　Bjontegaard　Delta　Bit　Rate,　and　bit　fluctuation　than　the　benchmarks,　which　validates　the　efficiency　of　the　proposed　method.