DGA Seminar: Franz Wirl

Franz Wirl
University of Vienna

Dynamic Games and Applications Seminar

On the Non-Uniqueness of Linear Markov Perfect Equilibria in Linear-Quadratic Differential Games: A Geometric Approach

February 22, 2024 11:00 AM — 12:00 PM (Montreal time)

Zoom webinar link

Although the possibility of multiple nonlinear equilibria in linear-quadratic differential games is extensively discussed, the literature on models with multiple linear Markov perfect equilibria (LMPEs) is scarce. And indeed, almost all papers confined to a single state (a very large majority of the application of differential games to economic problems) find a unique LMPE. This paper explains this finding and derives conditions for multiplicity based on the analysis of the phase plane in the state and the derivative of the value function. The resulting condition is applied to derive additional examples using pathways different from the (two) known ones. All these examples, more precisely, their underlying pathways, contradict usual assumptions in economic models. However, by extending the state space, we provide an economic setting (learning by doing) that leads to multiple LMPEs.