Conditional Viability for Impulse Differential Games |
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Authors: | Email author" target="_blank">Jean-Pierre?AubinEmail author Nicolas?Seube |
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Institution: | (1) Université de Paris-Dauphine, Place du Marchal de Lattre de Tassigny, 75775, PARIX cx 16, France;(2) ENSIETA, 29806, Brest cx 9, France |
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Abstract: | We introduce in this paper the concept of “impulse evolutionary game”. Examples of evolutionary games are usual differential
games, differentiable games with history (path-dependent differential games), mutational differential games, etc. Impulse
evolutionary systems and games cover in particular “hybrid systems” as well as “qualitative systems”. The conditional viability
kernel of a constrained set (with a target) is the set of initial states such that for all strategies (regarded as continuous
feedbacks) played by the second player, there exists a strategy of the first player such that the associated run starting
from this initial state satisfies the constraints until it hits the target. This paper characterizes the concept of conditional
viability kernel for “qualitative games” and of conditional valuation function for “qualitative games” maximinimizing an intertemporal
criterion. The theorems obtained so far about viability/capturability issues for evolutionary systems, conditional viability
for differential games and about impulse and hybrid systems are used to provide characterizations of conditional viability
under impulse evolutionary games. |
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Keywords: | impulse differential games differential games conditional viability Hamilton-Jacobi-Bellman-Isaacs quasi-variational inequalities |
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