International business (IB) literature on sustainability highlights the role of the state in fostering corporate green innovation to address grand challenges. Yet, the diversity of government initiatives and firm reactions underscores a gap in understanding the mechanisms behind heterogeneity in firm behavior and policy effectiveness. This study seeks to address this gap by exploring two critical yet underexamined questions. First, can government rewards and threats serve as dual insurance to spur green innovation? Second, how do firms differ in their responses to these rewards and threats? Leveraging two crucial government initiatives for corporate green innovation in China—environmental protection subsidies (rewards) and inspections (threats), we argue and demonstrate how government rewards and threats show a substitutive relationship for multinational enterprises (MNEs), but a complementary relationship for local firms. Our core argument is that rewards and threats from local governments create conflict for MNEs as they must balance the competing demands of diverse international stakeholders. In contrast, for local firms, these same policies generate synergy by aligning with the unified expectations of local stakeholders. Our analyses rules out alternative explanations and shed light on possible spillovers. This study brings novel insights into heterogeneous firm responses to government initiatives for tackling grand challenges.