<p>This paper examines how investment in potential breakthrough technologies for climate adaptation affects emissions and investment decisions in a strategic context. Using an N-player stochastic differential game, we solve for the subgame perfect Nash equilibrium under both symmetric and asymmetric assumptions. We find that the prospect of a breakthrough, enabled by knowledge investments that reduce future environmental damages, induces countries to increase current emissions, leading to a higher steady-state pollution stock. Greater likelihood of achieving a breakthrough further accelerates emissions accumulation. In asymmetric scenarios, countries with higher probabilities of success emit more in anticipation of future adaptive capacity, while others reduce emissions to compensate. These results suggest that optimism about future technologies, while potentially beneficial, can paradoxically worsen environmental degradation if not guided by a balanced policy framework. Moreover, the dynamics in asymmetric settings underscore the need for international collaboration to address disparities in technological advancement.</p>