arXiv:2610.12779v1 Announce Type: cross Abstract: Large-scale strategic systems, such as maintenance workflows, cyber campaigns, and multi-agent AI pipelines, consist of many interactions whose outcomes determine which later interactions become possible, who takes part, and with what resources. We introduce game Petri nets, formalized as outcome-driven compositional game Petri nets (OCGPNs), to model and analyze such systems. Local games are attached to places of a colored Petri net, and a game-to-token interface converts each resolved game into typed tokens that enable, synchronize, or block subsequent games. For general, concurrent nets, we give an operational semantics and a structural theory based on invariants and Farkas certificates, which shows that guards can certify unreachability whereas incentive instruments can only change values. For sequential nets, the net induces a stochastic game on its game places. We prove that global equilibria are exactly collections of equilibria of local games augmented by continuation values, characterize through successor-level pivotality when downstream games change upstream behavior, and compute values place by place via a decomposition into strongly connected components, at a cost additive in local game sizes. A composition calculus based on place fusion glues certificates across subnets and summarizes downstream subnets by their entry values. Two running examples, a maintenance workflow and an intrusion campaign derived from multi-resolution cyber-defense games, illustrate the theory, including the composition of a newly discovered attack scenario with an existing campaign.