Selection of equilibria in a linear quadratic mean-field game

• Published in: Stochastic processes and their applications Vol. 130; no. 2; pp. 1000 - 1040
• Main Authors: Delarue, François, Foguen Tchuendom, Rinel
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.02.2020; Elsevier
• Subjects: [formula omitted]-player game; Common noise; Mathematics; Mean-field game; Peano phenomenon; Probability; Selection of equilibria; Vanishing viscosity; secondary; Mean-field game; Selection of equilibria; Vanishing viscosity; Common noise; primary; N-player game; Peano phenomenon; Linear-quadratic control problem; Transition point; Scalar conservation law; N -player game; Burgers equation; Entropy solution

In this paper, we address an instance of uniquely solvable mean-field game with a common noise whose corresponding counterpart without common noise has several equilibria. We study the selection problem for this mean-field game without common noise via three approaches. A common approach is to selec...