Under extended producer responsibility (EPR) regulations, trade-in programs allow manufacturers to play a vital role in recycling. Simultaneously, third-party recyclers (TPRs) can use their recycling network to compensate for manufacturers having only a single recycling channel, which increases the competition between them. To study whether companies should authorize TPRs, we constructed and analyzed a Stackelberg game model with trade-in programs under EPR regulations by focusing on three different closed-loop supply chain (CLSC) structures and differentiating consumer categories. The analytical results showed that when the government does not act as the decision maker, the optimal product selling price of the manufacturer does not change under each strategy. Otherwise, the manufacturer’s decision is affected by the cost structure and amount of subsidy, as well as funds determined by the government under the optimal environmental benefit. Furthermore, when the residual value coefficient of the used products is high, manufacturers authorize TPRs to recycle used products.