In this study, we present models where participants strategically select their risk levels and earn corresponding rewards, mirroring real-world competition across various sectors. Our analysis starts with a normal form game involving two players in a continuous action space, confirming the existence and uniqueness of a Nash equilibrium and providing an analytical solution. We then extend this analysis to multi-player scenarios, introducing a new numerical algorithm for its calculation. A key novelty of our work lies in using regret minimization algorithms to solve continuous games through discretization. This groundbreaking approach enables us to incorporate additional real-world factors like market frictions and risk correlations among firms. We also experimentally validate that the Nash equilibrium in our model also serves as a correlated equilibrium. Our findings illuminate how market frictions and risk correlations affect strategic risk-taking. We also explore how policy measures can impact risk-taking and its associated rewards, with our model providing broader applicability than the Diamond-Dybvig framework. We make our methodology and open-source code available at https://github.com/louisabraham/cfrgame Finally, we contribute methodologically by advocating the use of algorithms in economics, shifting focus from finite games to games with continuous action sets. Our study provides a solid framework for analyzing strategic interactions in continuous action games, emphasizing the importance of market frictions, risk correlations, and policy measures in strategic risk-taking dynamics.

翻译：本研究提出了参与者策略性选择风险水平以获取相应收益的模型，模拟了现实世界各领域的竞争现象。我们从连续行动空间中的双人正规博弈入手，证实了纳什均衡的存在性与唯一性，并给出了解析解。随后将分析扩展到多人场景，提出了一种新的数值计算方法。本文的核心创新在于通过离散化方法使用遗憾最小化算法求解连续博弈。这一突破性方法使我们能够纳入市场摩擦与企业间风险相关性等现实因素。实验验证表明，本模型的纳什均衡同时也是相关均衡。研究结果揭示了市场摩擦与风险相关性如何影响策略性风险承担行为。我们还探讨了政策干预对风险承担及其收益的影响，相较戴蒙德-迪布维格框架，本模型具有更广泛的适用性。研究方法和开源代码已发布至https://github.com/louisabraham/cfrgame。在方法论层面，本文倡导将算法应用于经济学研究，将关注焦点从有限博弈转向连续行动集博弈。本研究为分析连续行动博弈中的策略互动提供了坚实框架，着重强调了市场摩擦、风险相关性及政策干预在策略性风险承担动态中的重要作用。