This paper introduces K-Level Reasoning, a novel approach for Large Language Models (LLMs) to enhance their dynamic reasoning capabilities in competitive and interactive environments. The study addresses the limitations of existing reasoning methods in dynamic settings that require k-level thinking, a concept not previously explored in LLMs. The research presents two well-defined game-based challenges, "Guessing 0.8 of the Average" and "Survival Auction Game," to evaluate LLMs' ability to reason dynamically. These challenges simulate real-world scenarios involving strategic decision-making, such as business strategy and stock market analysis. The K-Level Reasoning method incorporates cognitive hierarchy theory, enabling LLMs to recursively predict and respond to the thoughts and actions of rivals in competitive scenarios. By adopting the perspective of opponents and using historical information, the method significantly improves prediction accuracy and strategic decision-making. The approach is tested against various reasoning methods, including Chain-of-Thought (CoT), Reflexion, and Self-Refine, demonstrating superior performance in dynamic environments. Experiments show that K-Level Reasoning outperforms traditional methods in both games, particularly in adapting to changing strategies and predicting opponent actions. The method's recursive nature allows LLMs to anticipate multiple levels of strategic thinking, leading to more accurate and informed decisions. The study also highlights the importance of balancing depth of reasoning to avoid overthinking, which can lead to suboptimal outcomes. The research contributes to the field by establishing a robust benchmark for evaluating dynamic reasoning capabilities and demonstrating the effectiveness of K-Level Reasoning in complex, competitive scenarios. The findings suggest that integrating advanced reasoning methodologies can significantly enhance the dynamic reasoning abilities of LLMs, making them more effective in real-world applications involving strategic decision-making.This paper introduces K-Level Reasoning, a novel approach for Large Language Models (LLMs) to enhance their dynamic reasoning capabilities in competitive and interactive environments. The study addresses the limitations of existing reasoning methods in dynamic settings that require k-level thinking, a concept not previously explored in LLMs. The research presents two well-defined game-based challenges, "Guessing 0.8 of the Average" and "Survival Auction Game," to evaluate LLMs' ability to reason dynamically. These challenges simulate real-world scenarios involving strategic decision-making, such as business strategy and stock market analysis. The K-Level Reasoning method incorporates cognitive hierarchy theory, enabling LLMs to recursively predict and respond to the thoughts and actions of rivals in competitive scenarios. By adopting the perspective of opponents and using historical information, the method significantly improves prediction accuracy and strategic decision-making. The approach is tested against various reasoning methods, including Chain-of-Thought (CoT), Reflexion, and Self-Refine, demonstrating superior performance in dynamic environments. Experiments show that K-Level Reasoning outperforms traditional methods in both games, particularly in adapting to changing strategies and predicting opponent actions. The method's recursive nature allows LLMs to anticipate multiple levels of strategic thinking, leading to more accurate and informed decisions. The study also highlights the importance of balancing depth of reasoning to avoid overthinking, which can lead to suboptimal outcomes. The research contributes to the field by establishing a robust benchmark for evaluating dynamic reasoning capabilities and demonstrating the effectiveness of K-Level Reasoning in complex, competitive scenarios. The findings suggest that integrating advanced reasoning methodologies can significantly enhance the dynamic reasoning abilities of LLMs, making them more effective in real-world applications involving strategic decision-making.