From game theory to the control of multi-agent systems

Abstract: Motivated by the analysis of evolutive systems of agents with strategies, we enrich the structure of the celebrated replicator equation to include more realistic scenarios suitable for game-theoretic applications. In this context, non-linear continuity equations arise to describe the evolution of the mean-field limit of such systems. Starting from simple cases, we discuss more sophisticated models, which include the interplay between the evolution of the position of the players and the evolution of their strategies; the addition of a control factor that models the presence of a policy maker in multi-population dynamics, together with the rise and fall of leadership; the effects of an entropic regularisation in the system, as well as that of fluctuations.

We present the derivation of these equations, together with some well-posedness results.

MathematicsPhysics

Audience: researchers in the topic

Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor)