Iterated Games with LDL Goals over Finite Traces.

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 setting we study---iterated Boolean games with goals over finite traces (iBG_f)---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 games with LDL_f objectives is regular, and provides complexity results for the associated automata constructions.