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“Meet a GERAD researcher!” seminar

Nash Equilibria in Two-Player Differential Games with Impulse Control

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Jan 25, 2023   11:00 AM — 12:00 PM

Utsav Sadana Desautels Faculty of Management, McGill University, Canada

Utsav Sadana

Presentation on YouTube.

We study a class of deterministic finite-horizon two-player nonzero-sum differential games where players are endowed with different controls. We assume that Player 1 uses piecewise-continuous controls, while Player 2 uses impulse controls. For this class of games, we seek to derive conditions for the existence of feedback Nash equilibrium strategies for the players. More specifically, we provide a verification theorem for identifying such equilibrium strategies, using the Hamilton-Jacobi-Bellman (HJB) equations for Player 1 and the quasi-variational inequalities (QVIs) for Player 2. Further, we show that the equilibrium number of interventions by Player 2 is upper bounded. Furthermore, we specialize the obtained results to a scalar two-player linear-quadratic differential game. In this game, Player 1's objective is to drive the state variable towards a specific target value, and Player 2 has a similar objective with a different target value. We provide, for the first time, an analytical characterization of the feedback Nash equilibrium in a linear-quadratic differential game with impulse control. We illustrate our results using numerical experiments. (joint work with Puduru Viswanadha Reddy and Georges Zaccour)

Georges Zaccour organizer

Location

Hybrid seminar at GERAD
Zoom et salle 4488
Pavillon André-Aisenstadt
Campus de l'Université de Montréal
2920, chemin de la Tour

Montréal Québec H3T 1J4
Canada

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