2026/07/24 by Julia Butte, André Platzer
Computer Science · #acm:03B70 #acm:34A38 #acm:91A06 #acm:91A25 #cs.GT #cs.LO #msc:03B70 #msc:34A38 #msc:91A06 #msc:91A25
29 pages, 4 figures, version includes minor fixes of typos, etc
arxiv created 2026/07/29 · arxiv updated 2026/07/31
This paper introduces the three-player differential game logic dGL3, which enables the verification of hybrid games of discrete and differential equation dynamics with three players who may or may not form coalitions. Each player has an individual goal they try to fulfill, so the game becomes non-zero-sum when the goals of the players overlap. This is how dGL3 can verify complex situations involving multiple players, taking into account their coalitional power. dGL3 excels at verifying games where players share safety objectives but otherwise pursue different goals, so that they may or may not collaborate. In this case, zero-sum assumptions lead to overly conservative results by neglecting the potential of coordination amongst the players. In this paper, the syntax and semantics of dGL3 are presented and crucial properties of dGL3 are proved. A sound and relatively complete proof calculus for dGL3 is introduced and the use of dGL3 is illustrated in a canonical example.