In this paper we present an overview of the field of deterministic approximation of Markov
processes, both in discrete and continuous times. We will discuss mean field approximation …

This review presents and reviews various solved and open problems in developing,
analyzing, and mitigating epidemic spreading processes under human decision-making. We …

The lion's share of this chapter is devoted to the construction of equilibria for mean field
games with a common noise. We develop a general two-step strategy for the search of weak …

Mean Field Games (MFG) have been introduced to tackle games with a large number of
competing players. Considering the limit when the number of players is infinite, Nash …

Non-cooperative and cooperative games with a very large number of players have many
applications but remain generally intractable when the number of players increases …

Renewable energy sources such as wind and solar power have a high degree of
unpredictability and time-variation, which makes balancing demand and supply challenging …

We study infinite horizon discounted mean field control (MFC) problems with common noise
through the lens of mean field Markov decision processes (MFMDP). We allow the agents to …

A simple model of corruption that takes into account the effect of the interaction of a large
number of agents by both rational decision making and myopic behavior is developed. Its …

The well-known Cucker--Smale model is a macroscopic system reflecting flocking, ie, the
alignment of velocities in a group of autonomous agents having mutual interactions. In the …

Stochastic optimal control and games have a wide range of applications, from finance and
economics to social sciences, robotics, and energy management. Many real-world …