The existing and impending threats of climate change are ubiquitous and unequivocal. Whereas the threats of climate change are experienced by a number of sectors directly and indirectly, these threats are more prominent for the agriculture sector. The significantly higher vulnerability of agriculture to climate change triggers serious challenges for food security and the long-term development of multiple nations. The looming intensification of climate change in the foreseeable future is expected to amplify the aforementioned challenges, and therefore, addressing these challenges with opportune and effective countermeasures is the call of the hour. Existing literature identifies mitigation and adaptation as the most effective countermeasures in addressing the escalated vulnerability of agriculture to climate change. The effectiveness of agricultural mitigation and adaptation to climate change depends upon strategic interactions among multiple stakeholders, starting from farmers to policymakers. However, strategic interaction among farmers is instrumental in shaping farm-level mitigation and adaptation, especially since they are the final decision-makers regarding the adoption of mitigation or adaptation measures. Coordination and cooperation among farmers may eliminate the potential free-riding issues induced by the public good characteristics of agricultural mitigation. In contrast, farmers' cooperation can potentially reduce the overall costs associated with adaptation, ensuring higher profitability. This study underscores the significance of farmers' cooperation and develops a game-theoretic model to investigate how farmers' cooperation over farm-level mitigation and adaptation evolves over time. The theoretical investigation elucidates the critical role of relative costs and benefits in determining the stability of farmers' cooperation over mitigation and adaptation. The investigation further highlights the significance of higher-order punishments in disincentivising non-cooperation and encouraging strategic resource and information exchange among farmers to cut down adaptation costs. The study further employs Probit regression models to analyse survey data and examine whether they align with the theoretically derived conditions underpinning farmers' cooperation. The empirical analysis also emphasises the role of farmers' risk preferences along with several other factors in influencing their decisions to adopt technologies based on mitigation and adaptation. The estimated probit regression coefficients are observed to be in accordance with the theoretical conditions. The estimated coefficients also reveal that farmers' investment in mitigation practices is significantly influenced by their willingness to take risks and access to credit. In contrast, farmers' access to extension services, per capita household income and perceptions regarding climate change are estimated to be the significant factors determining farmers' adaptation. The findings of this study have critical policy implications towards promoting widespread agricultural mitigation and adaptation, which is expected to address the profound challenges driven by the elevated vulnerability of the sector to climate change.