Victory and defeat in differential games

Abstract

The author constructs the set-valued feedback map which allow players in a differential game the possibility of winning, separately or collectively, or the certainty of winning or loosing and characterizes the indicator functions of their graphs as solutions to (contingent) partial differential equations. Decisions are defined to be the derivatives of the controls of players, and decision rules for each of these set-valued feedback maps allowing the players to abide by them as time elapses are provided.