Past seminars

Prof. Tamer Başar
University of Illinois at Urbana-Champaign
Video | Slides

Multi-Agent Dynamical Systems with Asymmetric Information and with Elements of Learning

Decision making in dynamic uncertain environments with multiple agents arises in many disciplines and application domains, including control, communications, distributed optimization, social networks, and economics. Here a natural framework, and a comprehensive one, for modeling, optimization, and analysis is the one provided by stochastic dynamic games (SDGs), which accommodates different solution concepts depending on how the interactions among the agents are modeled, particularly whether they are in a cooperative mode (with the same objective functions, as in teams) or in a noncooperative mode (with different objective functions) or a mix of the two, such as teams of agents interacting noncooperatively across different teams (and of course cooperatively within each team). What also affects (strategic) interactions among the agents is the asymmetric nature of the information different agents acquire (and do not share or only partially share (selectively) with others, even within teams). What makes such problems even more challenging in a dynamic environment with networked agents is the dependence of the information available to one agent at some point in time on the policies or decisions of other agents who have already acted at earlier instants of time. Such decision problems, initially studied in a team framework, are known as those with nonclassical information where optimal policies of team agents must be designed to balance a tradeoff between contribution to optimality of the team objective function and signaling through their actions useful information to other agents in their neighborhood who would be acting after them. Existence of such a tradeoff between signaling and optimization creates even more challenging issues in SDGs with misaligned objectives among at least a subset of agents, which however can be addressed effectively for a specially structured subclass of such games, namely mean-field games.

This talk will provide an overview of the landscape above, first for a general class of stochastic dynamic teams and games, and then for a subclass where the objective functions are quadratic, and the interaction relationships are linear. The talk will also cover reinforcement learning embedded into policy development when agents do not have precise information on the underlying models.

Prof. Maryam Kamgarpour
EPFL

Learning equilibria in games with bandit feedback

A central challenge in large-scale engineering systems, such as energy and transportation networks, is enabling autonomous decision-making among interacting agents. Game theory provides a natural framework to model and analyze such problems. In practice, however, agents often have only partial information about the costs and actions of others. This makes decentralized learning a key tool for developing effective strategies. In this talk, I will discuss recent advances in decentralized learning for static and Markov games under bandit feedback. I will outline algorithms with convergence guarantees and highlight directions for future research.

Giona Fieni
ETH Zürich
Video

Game Theory in Formula One

Prof. David Fridovich-Keil
University of Texas at Austin
Video | Slides

Variations on a Theme: Information Structure, Equilibria, and Dynamic Games

This talk reviews a fundamental building block of dynamic game theory—the linear-quadratic game—and discuss how Nash equilibrium solutions differ as a consequence of the information players have access to at different times. In this context, we examine several recent results, aligned to the following questions:

How can we find feedback strategies which closely approximate Nash solutions, but minimize inter-agent communication/sensing?
If agents’ access to information changes during an interaction, are there scenarios in which we can still find equilibria efficiently?
In two-player, zero-sum games, there are classical results about the equivalence of solutions under different information structures for linear-quadratic games. In what sense do these extend beyond the linear-quadratic setting?

Dr. Benita Nortmann
EMPA - Swiss federal laboratories for material science and technology
Video | Slides

Exploring feedback Nash equilibria in infinite-horizon LQ dynamic games

Many modern processes involve real-time decisions in dynamic environments influenced by multiple decision makers with team-based and individual, potentially competitive objectives. Dynamic game theory captures interactions between such players and allows us to model and design decision strategies. We focus on the class of infinite-horizon, nonzero-sum, linear quadratic (LQ), discrete-time dynamic games, which are relevant in various engineering and economic applications. Linear feedback Nash equilibrium (FNE) solutions to such LQ games are characterised via the solutions of coupled algebraic matrix equations. While reminiscent of the algebraic Riccati equation arising in LQ optimal control, these coupled equations are generally difficult to solve and may admit multiple solutions with different outcomes.

To effectively employ dynamic games to model and design multi-player decisions, it is important to understand the existence, number, and properties of equilibria and to develop efficient computation methods. In this talk, we first build intuition for the number and properties of FNE solutions by considering games with scalar dynamics and inputs, using geometric arguments. We then discuss iterative methods to compute FNE solutions for general LQ games, and a data-driven approach, which enables players to jointly converge to a FNE solution without knowledge of each other’s control objectives.

Dr. Nicolas Lanzetti
Caltech Video | Slides

Strategically Robust Game Theory via Optimal Transport

In many game-theoretic settings, agents are challenged with taking decisions against the uncertain behavior exhibited by others. Often, this uncertainty arises from multiple sources, e.g., incomplete information, limited computation, bounded rationality. While it may be possible to guide the agents' decisions by modeling each source, their joint presence makes this task particularly daunting. Toward this goal, it is natural for agents to seek protection against deviations around the emergent behavior itself, which is ultimately impacted by all the above sources of uncertainty. To do so, we propose that each agent takes decisions in face of the worst-case behavior contained in an ambiguity set of tunable size, centered at the emergent behavior implicitly defined. This gives rise to a novel equilibrium notion, which we call strategically robust equilibrium. Building on its definition we show that, when judiciously operationalized via optimal transport, strategically robust equilibria
(i) interpolate between Nash and security strategies;
(ii) come at no additional computational cost compared to Nash equilibria;
(iii) often lead to better decisions and higher payoffs.
Through a variety of experiments including bi-matrix games, congestion games, and Cournot competition, we show that strategic robustness protects against uncertainty in the opponents' behavior and, surprisingly, results in higher equilibrium payoffs – an effect we refer to as coordination via robustification. Joint work with S. Fricker, S. Bolognani, F. Dörfler, and D. Paccagnan.