In many decision-making settings, a selfish agent seeks to optimize its benefit given some situational constraints. Mathematically, the agent often solves an optimization problem whose solution provides a prescriptive recommendation on the best decision. However, decision-making is rarely an individual task: each selfish decision-maker often interacts with other similarly self-interested decision-makers. We introduce the taxonomy of Mathematical Programming Games (MPGs), games where each agent decision problem is a parametric optimization problem expressing a heterogeneous and possibly complex set of constraints. MPGs offer a rigorous and powerful mathematical framework extending traditional tasks from Operations Research – to name a few, logistics, scheduling, and tactical decision-making – to a multi-agent setting. Furthermore, they also offer a novel perspective to frame the dynamics of strategic decision-making and help embed fairness mechanisms into the decision-making process. This talk overviews the challenges and opportunities MPGs offer, explicitly focusing on MPGs where players solve Mixed-Integer programs. We present a few motivating applications and discuss the leading algorithmic and theoretical schemes to compute, select and enumerate Nash equilibria.
Bio: I am a research associate at the Canada Excellence Research Chair in Data Science for Real-Time Decision-Making of Polytechnique Montréal. I hold a Ph.D. in Mathematics from Polytechnique Montréal, where I graduated in February 2022 with the thesis "Mathematical Programming Games". Before my doctorate, I completed a B.Sc. in Engineering and Management from Politecnico di Torino (Italy). My work aims at understanding the dynamics of multi-agent strategic decision-making in competitive settings where agents are solving optimization problems. From a high-level perspective, my research lies at the interface of Algorithmic Game Theory and Mathematical Optimization, and it analyzes strategic decision-making through the lenses of a unified framework integrating the two disciplines