Symbolic awards, such as low-carbon supplier certification, actively motivate suppliers to strengthen their carbon reduction initiatives and advance sustainable supply chain management. Yet, when low-carbon suppliers remain scarce, these awards intensify buyer competition and raise the costs of maintaining supplier relationships. Notably, several suppliers leverage awards to build reputations that improve their bargaining power, creating strategic dilemmas around public disclosure. This study develops a two-stage game model and tests its predictions through controlled experiments to examine how alternative award formats influence supplier and buyer outcomes. Our results show that a symbolic award significantly encourages suppliers to reduce emissions and improve buyers’ bottom lines. However, award format shapes buyer utility in critical ways: public awards compel buyers to invest more in retaining suppliers, while private awards deliver greater financial value to buyers. In markets with few low-carbon suppliers, buyers often need to allocate more resources to relationship management, while suppliers may resist private incentives if they perceive reputational drawbacks. These findings highlight the need for carefully designed disclosure strategies to balance costs and benefits for both sides, thereby fostering more effective and sustainable supply chains.