How to Manage a Budget with ATL+

Abstract

We study ATL+ enriched with one resource (written ATL+(1)) extending ATL+ with the possibility to manage a budget. We propose a game-theoretic semantics via the introduction of two evaluation games so that the compositional semantics is captured by strategies in the games. We show that the model-checking problem for ATL+(1) is in PSPACE and we identify fragments in PTIME. By-products of our investigations include a simplified PSPACE decision procedure for resource-free ATL+ based on small strategy skeletons, the synthesis of constraints in ATL+(1) with parameters and a PSPACE bound to solve a close energy game problem with one counter and objectives of temporal depth one.