Motivated by the growing activities that manufacturers are dedicating into remanufacturing, this paper examines the sharing strategies of remanufacturing design (RD) responsibility and the authorization strategies of remanufacturing. In this investigation, we developed three game models and analysed the equilibrium outcomes to define the conditions under which the remanufacturer and the manufacturer share RD responsibility. We further explored the impact of shared responsibility on the manufacturer's authorization strategies. The findings indicate that: (1) The authorized remanufacturer shares the RD responsibility and selectively remanufactures used products when the unit remanufacturing cost saving is low. (2) The manufacturer raises the authorization fee to receive a proportion of RD benefits when it undertakes RD responsibility individually. Although shared responsibility increases the authorization fee, it does not alter the proportion of RD benefits captured by the manufacturer. (3) Shared responsibility increases the remanufacturing ratio and profits of both stakeholders, effectively mitigating the free-riding problem. This study provides theoretical references for the remanufacturer on sharing RD responsibility and it also gives insights for the manufacturer to adjust their authorization decisions accordingly.