The continuity equation describes the transport of a distributed quantity along a vector field. If two independent players affect the vector field we arrive at a game with dynamics given by the continuity equation, or a game in the space of measures. For this game, we discuss a notion of program strategy, provide an existence theorem for the equilibrium, and prove a necessary equilibrium condition.
Program strategies for a dynamic game in the space of measures
Pogodaev, Nikolay
2018
Abstract
The continuity equation describes the transport of a distributed quantity along a vector field. If two independent players affect the vector field we arrive at a game with dynamics given by the continuity equation, or a game in the space of measures. For this game, we discuss a notion of program strategy, provide an existence theorem for the equilibrium, and prove a necessary equilibrium condition.
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