Marianne Akian- Tropical Linear Regression and Mean Payoff Games or How to Measure the Distance to Equilibria

Explore a 32-minute lecture on tropical linear regression and its connection to mean payoff games. Delve into the study of approximating point sets with tropical hyperplanes, uncovering a strong duality theorem that links the problem's value to the maximal radius of a Hilbert's ball in tropical polyhedra. Discover the polynomial-time equivalence between this regression problem and mean payoff games, and examine variations involving signed tropical hyperplanes. Learn how these concepts apply to auction theory, where tropical hyperplanes represent equilibrium prices, allowing for quantification of market distance from equilibria and inference of decision-maker preferences. Based on joint work with Stephane Gaubert, Yang Qi, and Omar Saadi, this talk provides insights into cutting-edge mathematical research with practical applications in economics and game theory.