Qualitative Differential Games: A Viability Approach

Aubin, J.-P. (1988). Qualitative Differential Games: A Viability Approach. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-88-033

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Abstract

The author defines the playability property of a qualitative differential game, defined by a system of differential equations controlled by two controls. The rules of the game are defined by constraints on the states of each player depending on the state of the other player. This paper characterizes the playability property by a regulation map which associates with any playable state a set of playable controls.

In other words, the players can implement playable solutions to the differential game by playing for each state a static game on the controls of the regulation subset.

One must extract among theses playable controls the set of discriminating and pure controls of one of the players. Such controls are defined through an adequate "contingent" Hamilton-Jacobi-Isaacs equation. Sufficient conditions implying the existence of continuous or minimal playable, discriminating and pure feedbacks are provided.

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