  This article introduces differential hybrid games, which combine differential
games with hybrid games. In both kinds of games, two players interact with
continuous dynamics. The difference is that hybrid games also provide all the
features of hybrid systems and discrete games, but only deterministic
differential equations. Differential games, instead, provide differential
equations with continuous-time game input by both players, but not the luxury
of hybrid games, such as mode switches and discrete-time or alternating
adversarial interaction. This article augments differential game logic with
modalities for the combined dynamics of differential hybrid games. It shows how
hybrid games subsume differential games and introduces differential game
invariants and differential game variants for proving properties of
differential games inductively.
