Many new product platforms now engage in secondhand markets using two models. Consumers incurring transaction costs can trade used products with each other (the C2C model); instead, platforms can bear transaction costs to buy back and resell used products (the BR model). Meanwhile, new products may be sold under reselling, i.e., platforms retail products wholesaled by manufacturers, or under agency selling, i.e., manufacturers sell products directly by paying commission fees. We consider a supply chain with a manufacturer and a platform who decides whether to introduce secondhand markets and which model to adopt under different selling formats. We conduct game-theoretic analysis and find that under reselling the platform should adopt the C2C or the BR model only when this increases the new product demand, i.e., when product durability is large. However, under agency selling, both models can benefit the platform by increasing either the new product price or demand when the product durability is not too small but the transaction cost is small. Furthermore, the BR model sometimes can benefit the platform by generating used product revenue. Regardless of different selling formats, the platform should choose the secondhand market model with a relatively low transaction cost even though it does not endure this cost in the C2C model; both models can yield a win-win outcome for the platform and the manufacturer as long as the product durability is large and the transaction cost is small. Finally, introducing a secondhand market makes the manufacturer less likely to adopt agency selling.