Relying　on　the　computation　offloading　technology,　edge　computing　has　shown　potential　in　countless　tasks　processing　in　the　industrial　Internet　of　Things　(IIoT),　which　is　composed　of　multiple　edge　clouds　and　multiple　IIoT　devices.　Nevertheless,　with　increasing　demands　for　computation　service,　how　to　design　reliable　transmission　mechanism　and　allocate　proper　computation　resource　has　become　bottlenecks.　In　this　article,　we　propose　a　computation　offloading　mechanism　based　on　two-stage　Stackelberg　game　to　analyze　the　interaction　between　multiple　edge　clouds　and　multiple　IIoT　devices.　To　be　specific,　the　edge　clouds　are　denoted　as　leaders　who　set　the　appropriate　price　for　their　computation　resource.　Besides　considering　the　payment　cost,　the　IIoT　devices　which　are　termed　as　the　followers　formulate　their　utility　function　by　considering　the　social　interaction　information　from　the　potential　IIoT　devices.　The　existence　and　uniqueness　of　the　Stackelberg　equilibrium　are　analyzed　considering　two　possible　cases,　i.e.,　complete　information　and　incomplete　information.　Moreover,　two　dynamic　iterative　algorithms　are　invoked　for　solving　both　problem　models,　respectively.　Finally,　experimental　results　show　that　our　proposed　scheme　is　conducive　to　seeking　the　appropriate　price　and　computation　requirement.　Besides,　social　interaction　information　plays　an　important　role　in　achieving　a　reasonable　computation　requirement　for　IIoT　devices.