Strategically Robust Game Theory via Optimal Transport

Abstract

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 so 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 for all players – an effect we refer to as coordination via robustification.

Joint work with: Sylvain Fricker, Saverio Bolognani, Florian Dörfler, and Dario Paccagnan.

Biography

Nicolas Lanzetti is a Ph.D. candidate at the Automatic Control Laboratory at ETH Zürich under the supervision of Prof. Dörfler (main advisor) and Prof. Figalli (second advisor). He received the B.Sc. and the M.Sc. in mechanical engineering, with a focus on Robotics, Systems, and Control from ETH Zurich in 2016 and 2019, respectively. He was a visiting researcher at the Massachusetts Institute of Technology and Stanford University. Inspired by challenges in electricity markets, robotic coordination, and biology, his research develops theoretical foundations and algorithms for strategic decision-making under uncertainty, using and advancing techniques in optimal transport, optimization, and game theory. He is the recipient of the Willi Studer Prize, the ETH Medal and the SVOR/ASRO award for his Master’s thesis, and the Best Paper Award (1st Place) at the 2021 IEEE International Conference on Intelligent Transportation Systems.