Multi-Player Games with LDL Goals over Finite Traces

Abstract Linear Dynamic Logic on finite traces ( LDL F ) is a powerful logic for reasoning about the behaviour of concurrent and multi-agent systems. In this paper, we investigate techniques for both the characterisation and verification of equilibria in multi-player games with goals/objectives expressed using logics based on LDL F . This study builds upon a generalisation of Boolean games, a logic-based game model of multi-agent systems where players have goals succinctly represented in a logical way. Because LDL F goals are considered, in the settings we study—Reactive Modules games and iterated Boolean games with goals over finite traces—players' goals can be defined to be regular properties while achieved in a finite, but arbitrarily large, trace. In particular, using alternating automata, the paper investigates automata-theoretic approaches to the characterisation and verification of (pure strategy Nash) equilibria, shows that the set of Nash equilibria in multi-player games with LDL F objectives is regular, and provides complexity results for the associated automata constructions.