Non-Smooth and Discontinuous Markov Perfect Nash Equilibrium in Differential Games

Explore advanced game theory concepts in this 53-minute research seminar that establishes necessary and sufficient conditions for characterizing Markov Perfect Nash Equilibrium (MPNE) in differential games where equilibrium solutions may exhibit piecewise smoothness with respect to state variables. Learn how the classical framework connects with Rankine-Hugoniot jump conditions from fluid dynamics to analyze weak solutions of differential game equations. Discover how entropy conditions under strict concavity assumptions enable identification of unique MPNE solutions from multiple candidate profiles that satisfy weak solution criteria. Examine a practical application through a finite-horizon differential game modeling non-cooperative management of non-renewable resources, demonstrating how non-concave utility functions at final time periods generate discontinuous equilibrium strategies. Gain insights into the mathematical foundations linking optimal control theory, fluid dynamics principles, and game-theoretic solution concepts for complex dynamic strategic interactions.