Game and Network Theory: Equilibrium Analysis, Learning, and Intervention Design

Francesca Parise

Recent Trends in Fair Division

Frédéric Meunier

Many natural and engineering multi-agent systems are characterized by the presence of a large number of users interacting in complex and heterogeneous ways. Examples include sellers competing in online markets, people interacting over social networks or AI-agents supporting automated decision making. This course will discuss fundamental mathematical models that can be used to study these systems, predict their overall outcome and plan interventions aimed at improving performance, security, efficiency and welfare. To this end, the course will introduce fundamental tools from game theory to model strategic agent decision making and tools from network theory and graph limits to model agents’ interactions. Such tools will be used to study equilibrium outcomes, learning and intervention design, with specific focus on settings involving very large populations.

A central question in social choice theory is how to allocate items or tasks among people fairly. This seemingly simple objective raises several fundamental challenges: What does fairness mean? Do fair allocations exist? How can they be computed? Addressing these questions has led to fruitful interactions between several disciplines---including computer science, economics, political science, and topology---and to a rich body of results and techniques. This course aims to provide a gentle introduction to fair division, from classical results to recent developments. We will explore some of the main techniques used in the area, as well as the main open problems that remain. A particular focus of the course will be on envy-freeness, one of the most natural and extensively studied notions of fairness. Along the way, we will encounter some elegant connections with mathematics, in particular with combinatorics and topology.