A Game of Competition for Risk

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

Reinforcement Learning and Game Theory for Smart Grid Security

This dissertation focuses on one of the most critical and complicated challenges facing electric power transmission and distribution systems which is their vulnerability against failure and attacks. Large scale power outages in Australia (2016), Ukraine (2015), India (2013), Nigeria (2018), and the United States (2011, 2003) have demonstrated the vulnerability of power grids to cyber and physical attacks and failures. These incidents clearly indicate the necessity of extensive research efforts to protect the power system from external intrusion and to reduce the damages from post-attack effects. We analyze the vulnerability of smart power grids to cyber and physical attacks and failures, design different gametheoretic approaches to identify the critical components vulnerable to attack and propose their associated defense strategy, and utilizes machine learning techniques to solve the game-theoretic problems in adversarial and collaborative adversarial power grid environment. Our contributions can be divided into three major parts:Vulnerability identification: Power grid outages have disastrous impacts on almost every aspect of modern life. Despite their inevitability, the effects of failures on power grids’ performance can be limited if the system operator can predict and identify the vulnerable elements of power grids. To enable these capabilities we study machine learning algorithms to identify critical power system elements adopting a cascaded failure simulator as a threat and attack model. We use generation loss, time to reach a certain percentage of line outage/generation loss, number of line outages, etc. as evaluation metrics to evaluate the consequences of threat and attacks on the smart power grid.Adversarial gaming in power system: With the advancement of the technologies, the smart attackers are deploying different techniques to supersede the existing protection scheme. In order to defend the power grid from these smart attackers, we introduce an adversarial gaming environment using machine learning techniques which is capable of replicating the complex interaction between the attacker and the power system operators. The numerical results show that a learned defender successfully narrows down the attackers’ attack window and reduce damages. The results also show that considering some crucial factors, the players can independently execute actions without detailed information about each other.Deep learning for adversarial gaming: The learning and gaming techniques to identify vulnerable components in the power grid become computationally expensive for large scale power systems. The power system operator needs to have the advanced skills to deal with the large dimensionality of the problem. In order to aid the power system operator in finding and analyzing vulnerability for large scale power systems, we study a deep learning technique for adversary game which is capable of dealing with high dimensional power system state space with less computational time and increased computational efficiency. Overall, the results provided in this dissertation advance power grids’ resilience and security by providing a better understanding of the systems’ vulnerability and by developing efficient algorithms to identify vulnerable components and appropriate defensive strategies to reduce the damages of the attack

Inverse Dynamic Game Methods for Identification of Cooperative System Behavior

Die dynamische Spieltheorie hat sich als ein effektiver Ansatz zur Modellierung und Analyse der Interaktion zwischen mehreren Akteuren oder Spielern in dynamischen Prozessen erwiesen. Um diese Theorie in realen Anwendungen umzusetzen, ist jedoch die Möglichkeit einer schnellen Identifikation der Ziele jedes Spielers entscheidend. Dieses Identifikationsproblem wird als inverses dynamisches Spiel bezeichnet. Hierfür präsentiert diese Dissertation Lösungen, die auf Beobachtungen der Spieleraktionen und der resultierenden Zustandstrajektorie basieren, welche die Entwicklung des Spiels über die Zeit beschreibt. Es werden zwei Arten von Methoden zur Lösung von inversen dynamischen Spielen entwickelt. Die erste besteht in der Anwendung von regelungstechnischen Methoden. Für die weitverbreitete Klasse der linear-quadratischen dynamischen Spiele werden zusätzlich explizite Mengen formuliert, die alle möglichen Lösungen des inversen Problems beschreiben. Der zweiten Methode liegen Verfahren des Inverse Reinforcement Learnings aus der Informatik zugrunde. Für beide Arten von Methoden werden mathematische Bedingungen formuliert, unter denen eine erfolgreiche Schätzung der Ziele aller Spieler garantiert ist. Ein simulativer Vergleich mit einem Verfahren aus dem Stand der Technik zeigt die höhere Effizienz der vorgestellten neuen Ansätze. Darüber hinaus werden die Methoden für die Identifikation von kooperativem menschlichen Verhalten in einem Lenkmanöver angewendet. Die entwickelten Ansätze für inverse dynamische Spiele ermöglichen die effiziente Identifikation von Spielerzielen und können in zahlreichen Anwendungsfeldern wie beispielsweise der Mensch-Maschine-Interaktion und der Verhaltensbeschreibung biologischer Systeme eingesetzt werden

Adaptive Dynamic Programming: Solltrajektorienfolgeregelung und Konvergenzbedingungen

In this work, discrete-time and continuous-time methods that integrate flexible reference trajectory representations into Adaptive Dynamic Programming approaches are presented and analyzed for the first time. Moreover, theoretical conditions on the system state are derived that ensure the persistent excitation property, which is crucial for the convergence of the adaptation. Real-world applications of the presented adaptive optimal trajectory tracking control methods reveal their potential