Deployment　of　caching　in　wireless　networks　has　been　considered　an　effective　method　to　cope　with　the　challenge　brought　on　by　the　explosive　wireless　traffic.　Although　some　research　has　been　conducted　on　caching　in　cellular　networks,　most　of　the　previous　works　have　focused　on　performance　optimization　for　content　caching.　To　the　best　of　our　knowledge,　the　problem　of　caching　resource　sharing　for　multiple　service　provider　servers　(SPSs)　has　been　largely　ignored.　In　this　paper,　by　assuming　that　the　caching　capability　is　deployed　in　the　base　station　of　a　radio　access　network,　we　consider　the　problem　of　caching　resource　sharing　for　multiple　SPSs　competing　for　the　caching　space.　We　formulate　this　problem　as　an　oligopoly　market　model　and　use　a　dynamic　non-cooperative　game　to　obtain　the　optimal　amount　of　caching　space　needed　by　the　SPSs.　In　the　dynamic　game,　the　SPSs　gradually　and　iteratively　adjust　their　strategies　based　on　their　previous　strategies　and　the　information　given　by　the　base　station.　Then　through　rigorous　mathematical　analysis,　the　Nash　equilibrium　and　stability　condition　of　the　dynamic　game　are　proven.　Finally,　simulation　results　are　presented　to　show　the　performance　of　the　proposed　dynamic　caching　resource　allocation　scheme.