Nash Equilibria in Two-Player Differential Games with Impulse Control - Lecture

Explore Nash equilibria in two-player differential games with impulse control through this 51-minute seminar presented by Utsav Sadana from McGill University's Desautels Faculty of Management. Delve into the study of deterministic finite-horizon nonzero-sum games where players use different control strategies. Learn about the conditions for feedback Nash equilibrium strategies, including the Hamilton-Jacobi-Bellman equations and quasi-variational inequalities. Discover the upper bound on Player 2's interventions and examine a specialized scalar two-player linear-quadratic differential game. Gain insights into the analytical characterization of feedback Nash equilibrium in linear-quadratic games with impulse control, illustrated through numerical experiments. Follow the comprehensive outline covering real-world examples, state dynamics, literature review, strategy concepts, and future research directions in this GERAD Research Center presentation.

Intro
About me
Outline
Real-world example of impulse control
When to introduce new regulations?
State dynamics
Differential game with impulse control
Literature: Differential games with impulse control
Strategy and Nash equilibrium
Information structure and Nash equilibrium
Feedback Nash equilibrium [Sadana et al.TAC'22]
Threshold-type intervention policy
How to construct the continuation set?
Complementarity condition
Optimal control problem of Player I
A scalar linear-quadratic game
Assumptions
Player 2's optimality conditions
Numerical examples
Future research directions