Dynamic Games in Management

该研究计划的目标是开发数学模型和有效的计算算法，以解决动态和不确定环境下的实际战略决策问题。将考虑两个具体的应用领域：投资融资和自然资源管理。虽然这些应用领域彼此差别很大，但它们有一个共同的方法方法，即多维框架中的随机动态优化。在这两个领域，解决实际问题需要发展有效的数值方法。因此，除了解决这些具体问题外，本研究计划的更广泛目标是开发用于数值解决大规模随机动态问题和多阶段动态博弈的创新方法，从而促进不确定性决策领域的知识进步。在2008年金融危机之后，投资融资中的两个重要问题是管理风险和确保遵守相应的监管要求（例如，调整资本费用以考虑交易对手风险）。虽然投资金融具有动态游戏的所有基本成分，投资者、公司和金融中介机构具有竞争利益，并随着时间的推移进行战略互动，但大多数估值模型都是从单一角度构建的。我们的第一线研究目标是在估值和对冲模型中纳入战略维度，并开发新的计算方法，可用于涉及多维投资组合的现实场景。在实践中，用于风险管理和法规遵从的程序必须实时使用，并应在几秒钟内提供准确的结果。对环境和资源管理的日益关注与所谓的公地悲剧有关。对共同资源（空气质量、生物多样性、公海捕鱼）的获取导致过度开发，并可能造成灾难性后果。防止这种情况发生的手段之一是在利益攸关方之间达成协议（例如联合国主持下的多边协议），以确保资源的管理符合包括子孙后代在内的所有人的最佳利益。我们的第二个研究方向是研究环境协议的设计、稳定性和可执行性如何受到动态和不确定性以及参与者的远见和战略前景的影响。在这种情况下，前瞻被定义为参与者解释关键特征（环境破坏成本、学习、技术进步、签署国数量、经济发展）随时间演变的能力，而这种演变取决于参与者的联合策略。在实践中，增加预见性转化为多维模型。

The objective of this research program is to develop mathematical models and efficient computational algorithms to solve practical strategic decision-making problems in a dynamic and uncertain context. Two specific application areas will be considered: investment finance and natural resource management. Although these application areas are very different from each other, they share a common methodological approach, that is, stochastic dynamic optimization in a multidimensional framework. In both these areas, solving realistic problems requires the development of efficient numerical methods. Thus, in addition to addressing these specific issues, a broader objective of this research program is to develop innovative methods for numerically solving large-scale stochastic dynamic problems and multi-stage dynamic games, thereby contributing to the advancement of knowledge in the field of decision-making under uncertainty. In the aftermath of the 2008 financial crisis, two important issues in investment finance are managing risk and ensuring compliance with the corresponding regulatory requirements (e.g. capital charge adjustments to account for counterparty risk). While investment finance has all the essential ingredients of dynamic games, where investors, firms, and financial intermediaries have competing interests and interact strategically over time, most valuation models are built from a single perspective. The objectives of our first line of research are to incorporate a strategic dimension in valuation and hedging models, and to develop new computational methods that can be used for realistic scenarios involving multidimensional investment portfolios. In practice, procedures used for risk management and regulatory compliance must be used in real time and should provide accurate results within seconds. A growing concern in environmental and resource management is related to the so-called tragedy of the commons. Access to a common resource (air quality, biodiversity, high-seas fishing) leads to overexploitation and, potentially, to catastrophic consequences. One of the means employed to prevent this from happening is the establishment of agreements between stakeholders (e.g. multilateral agreements under the aegis of the United Nations), to ensure that resources are managed in the best interest of all, including future generations. The objective of our second line of research is to study how the design, stability and implementability of environmental agreements are affected by dynamics and uncertainty, and by the participants' foresight and strategic outlooks. In this context, foresight is defined as the players' ability to account for the evolution over time of key features (environmental damage costs, learning, technological progress, number of signatories, economic development), when this evolution depends on the players' joint strategies. In practice, increasing foresight translates into multidimensional models.