<p>The platform serves a dual role, as both an e-retailer and a marketplace provider, broadens the range of selling modes available to businesses and results in diverse co-opetitive structures, which complicates the interactions among supply chain members. Although a significant portion of literature has concentrated on selling mode choice, insufficient attention has been paid to the equilibrium that exists between manufacturers and retailers. This paper aims to address this gap by examining equilibrium from a platform-oriented co-opetitive perspective. Our results reveal that each of the four game models can reach to an equilibrium under certain conditions, however, the region achieving equilibrium tends to diminish as competition intensifies. Interestingly, we find that the platform’s profit may initially increase and then decrease with the commission rate when the manufacturer chooses agency selling while the retailer opts for direct selling. This observation implies that an excessively high commission rate could ultimately be detrimental to the platform. Finally, we analyze consumer surplus and social welfare across different models and explore the conditions that enable these members to maximize their profits.</p>