Abstract : Dynamic games and control theory involve the study of how multiple agents make decisions and interact strategically over time. These problems have traditionally been challenging to solve. This mini-symposium focuses on the latest developments in dynamic games and control theory enabled by data science. We will discuss how learning-based control theory has advanced the field, as well as the connection between reinforcement learning and dynamic games. Additionally, we will explore how these advances are enabling new applications in autonomous systems, networked systems, cyber-physical systems, and mathematical finance. This symposium will foster innovative interdisciplinary research that potentially can break new ground.
[03672] The Role of Information Structure in Games and Learning
Format : Talk at Waseda University
Author(s) :
Quanyan Zhu (New York University)
Abstract : The information structure of dynamic multi-agent systems plays a crucial role in determining the observation patterns of states, actions, and payoffs during interactions between agents. Differences in information structure can lead to surprising outcomes in a game. This talk aims to explore the role of information in dynamic games and learning. Specifically, we introduce the concept of the "price of information" and the "price of transparency" to quantify the gain or loss under different information patterns. We will discuss how information affects the strategic learning process, in which agents form beliefs based on their observations and generate policies based on those beliefs. Additionally, we will present how informational design can be used to incentivize agents and achieve the designer's goals at equilibrium in multi-agent systems.
[02854] Optimal transaction mechanism for dynamic storage management game in smart grid
Format : Talk at Waseda University
Author(s) :
Yasuaki Wasa (Waseda University)
Abstract : In this talk, we discuss an optimal transaction mechanism for a dynamic storage management game in smart grids in order to minimize the imbalance penalty charge of the grid in the wholesale electricity market. Our proposed mechanism is inspired by the primal-dual decomposition technique and the contract theory in economics. First, we present that the optimal power charge control profiles of the storage devices constitute a dynamic market equilibrium with a real-time pricing mechanism in a distributed fashion. Under the linear-quadratic dynamic grid model, the optimal design of the reference adjustment to modify the real-time pricing mechanism is analytically derived. The effectiveness of our proposed mechanism is also illustrated and discussed through simulation.
[02858] Reinforcement Learning Algorithm for Mixed Mean Field Control Games
Format : Online Talk on Zoom
Author(s) :
Jean-Pierre Fouque (University of California Santa Barbara)
Abstract : We present a new combined Mean Field Control Game (MFCG) problem which can be interpreted as a competitive game between collaborating groups and its solution as a Nash equilibrium between the groups. We propose a reinforcement learning algorithm to approximate the solution of such mixed Mean Field Control Game problems. We test the algorithm on benchmark linear-quadratic specifications for which we have analytic solutions.
Joint work with A. Angiuli, N. Detering, Mathieu Laurière, and J. Lin
[02930] Recent Advances on Fractional Optimal Control Problems
Format : Talk at Waseda University
Author(s) :
Jun Moon (Hanyang University)
Abstract : In this talk, we study recent results on fractional control problems. We first consider the fractional optimal control problem with terminal and running state constraints in finite dimensions. Then we study the fractional optimal control problem (without state constraints) in infinite dimensions described by fractional evolution equations. For both problems, we obtain the Pontryagin maximum principle, which constitutes the necessary condition for optimality.
Abstract : We investigate the stabilizability of Nash equilibrium of the game-based control system (GBCS), which was first introduced to model control systems whose structures involve rational agents. The stabilizability problem is whether the regulator can stabilize the system by regulating the Nash equilibrium formed by the agents. Some explicit conditions on the stabilizability of GBCS are given, by investigating the solvability relationship between the associated algebraic Riccati equations (AREs) and the algebraic Riccati inequalities (ARIs).
[04475] Cooperation and Cost Sharing Problems in Supply Networks
Format : Talk at Waseda University
Author(s) :
Sanjith Gopalakrishnan (McGill University)
Sriram Sankaranarayanan (Indian Institute of Management, Ahmedabad)
Abstract : Across several contexts such as supply chain security or traceability, costly actions by firms can yield payoffs to other firms in the network. Such positive externalities imply network-wide cooperative strategies can yield improvements over firms independently choosing individually-rational actions. However, cooperation can be hindered by disagreements over cost-sharing arrangements. In this talk, we review two recent applications and develop a general framework to identify implementable cost sharing mechanisms that can sustain network-wide cooperative actions.
[03268] Hodge allocation for cooperative rewards
Format : Online Talk on Zoom
Author(s) :
Tongseok Lim (Purdue University)
Abstract : Lloyd Shapley's cooperative value allocation theory is a central concept in game theory that is widely used in various fields to allocate resources and assess individual contributions. The Shapley formula and axioms that characterize it form the foundation of the theory.
Shapley value can be assigned only when all players are assumed to eventually form the grand coalition. We discuss how to extend Shapley's theory to account for value allocation in every partial coalition state.
