Min LQG Games and Collective Discrete Choice Problems in Decision Making

Watch a 42-minute lecture by Prof. Roland Malhamé from École Polytechnique de Montréal exploring finite horizon linear quadratic Gaussian games and their applications in collective discrete choice problems. Delve into two distinct cases of decision-making under social pressure: the zero noise "deterministic" case and the fully stochastic case. Learn how these mathematical models can be applied to understand opinion swings in elections, dynamics of societal choices, and micro-robotic exploration. Discover how e-Nash equilibria exist in both scenarios, with decentralized agent control strategies characterized by fixed points of specific finite dimensional operators. Understand how agent destination choices differ between the two cases, being fixed at the outset in the deterministic case while evolving probabilistically in the stochastic case. Benefit from Prof. Malhamé's extensive expertise in statistical mechanics approaches to large-scale systems analysis, aggregate electric load modeling, and mean field games theory, gained through his distinguished career spanning multiple international institutions.