With　the　construction　and　development　of　space-air-ground　integrated　information　networks，　the　global　coverage　of　wireless　networks　and　ubiquitous　artificial　intelligence　have　become　possible.　As　space-based　edge　computing　nodes，satellites　and　UAVs　can　assist　ground　servers　to　complete　various　tasks.　These　applications　become　important　application　scenarios　in　6G　networks.　The　current　research　on　satellite　and　UAV　edge　computing　is　in　the　initial　stage.　Edge　computing　services　provided　by　satellites　and　UAVs　still　need　deep　analysis　and　detailed　modeling　in　terms　of　service　modes　and　practical　applications.　Since　computing　hardware　of　satellites　and　UAVs　is　scarce　and　expensive，one　single　node　usually　difficult　to　provide　complex　data　processing　services　independently.　Existing　resource　management　algorithms　for　satellites　and　UAVs　focus　on　the　full　utilization　of　hardware　resources.　These　algorithms　usually　require　multiple　rounds　to　converge　the　optimal　solution.　In　the　distributed　scenario　of　space-air-ground　integrated　network　applications，　these　algorithms　are　difficult　to　meet　the　requirements　of　rapid　convergence.　To　solve　the　above　problems，　this　paper　focuses　on　the　integration　of　multi-node　resources　and　efficient　resource　management　methods　based　on　the　distributed　scenario　of　space-based　edge　computing.　Based　on　the　satellite　computing　capability　of　Tiansuan　constellation，this　paper　analyzes　the　service　mode　of　space-based　resources　in　the　space-air-ground　integrated　networks.　Two　modes　of　computing　service　integration　named　composition　and　aggregation　are　proposed.　According　to　these　two　service　integration　modes，this　paper　present　general　computing　tasks　and　special　computing　tasks.　To　accomplish　these　tasks，　computing　resource　management　are　described　as　two　types　of　service　renting.　Based　on　practical　application　scenarios，we　model　these　service　rent　processes　as　two-stage　Stackelberg　games　and　establish　the　utility　functions　of　user　devices　and　edge　nodes.　We　analyze　the　Stackelberg　games　of　two　types　of　renting　services　and　prove　the　existence　of　Nash　equilibrium.　To　solve　the　slow　converges　problem　in　the　existing　two-stage　dynamic　iterative　algorithm，we　propose　two　distributed　algorithms.　One　is　distributed　hybrid　dynamic　iterative　algorithm　and　the　other　is　distributed　grouping　dynamic　iterative　algorithm.　These　algorithms　only　need　one　stage　of　dynamic　iteration　to　obtain　the　optimal　pricing　scheme　of　edge　computing　resources　and　the　optimal　resource　renting　strategy　of　user　devices.　The　proposed　algorithms　aim　to　reduce　the　number　of　iterations　between　edge　computing　nodes　and　user　equipments.　Less　iterations　will　speed　up　the　convergence　speed　of　the　game　process.　To　verify　the　performance　of　the　proposed　method，this　paper　constructs　a　simulation　experiment　based　on　distributed　scenarios.　Under　the　setting　of　typical　parameters，we　analyze　the　resource　allocation　results，the　utility　of　user　devices　and　edge　nodes，　and　the　convergence　speed　of　the　algorithm.　The　simulation　results　show　that　the　proposed　method　can　achieve　the　optimal　allocation　of　space-based　edge　computing　resources，　and　enhance　the　applicability　of　the　algorithm　in　real　space-air-ground　integrated　information　network　scenarios.　Under　two　different　computing　service　modes，　the　proposed　method　can　maximize　the　benefits　of　edge　computing　service　providers　and　consumers；Compared　with　the　related　research　in　recent　years，the　convergence　time　of　the　proposed　method　can　be　reduced　by　more　than　60%.　©　2023　Science　Press.　All　rights　reserved.