Semi-Competitive Differential Game Logic

Abstract: This paper introduces semi-competitive differential game logic dGLsc, which makes it possible to specify and verify games on hybrid systems with two players that may collaborate with each other when helpful and may compete when necessary. Unlike in zero-sum games, the players in the hybrid games of dGLsc have individual goals that may overlap leading to nonzero-sum games. dGLsc solves the subtlety that even though each player may benefit from knowledge of the other player's goals, e.g., concerning shared safety objectives, the resulting hybrid system would still be unsafe if every player were to mutually assume the other player would control to avoid unsafety. The syntax and semantics, as well as a sound and relatively complete proof calculus are presented for dGLsc. The relationship between dGLsc and zero-sum differential game logic dGL is discussed and the purpose of dGLsc illustrated in a canonical example.