Literature: Differential games with impulse control
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Strategy and Nash equilibrium
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Information structure and Nash equilibrium
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Feedback Nash equilibrium [Sadana et al.TAC'22]
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Threshold-type intervention policy
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How to construct the continuation set?
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Complementarity condition
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Optimal control problem of Player I
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A scalar linear-quadratic game
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Assumptions
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Player 2's optimality conditions
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Numerical examples
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Future research directions
Description:
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.
Nash Equilibria in Two-Player Differential Games with Impulse Control - Lecture