Abstract
In this paper, we investigate the rational synthesis problem for concurrent game structures for a variety of objectives ranging from reachability to Muller condition. We propose a new algorithm that establishes the decidability of the non cooperative rational synthesis problem that relies solely on game theoretic techniques as opposed to previous approaches that are logic based. Given an instance of the rational synthesis problem, we construct a zero-sum turn-based game that can be adapted to each one of the class of objectives. We obtain new complexity results. In particular, we show that in the cases of reachability, safety, Büchi, and co-Büchi objectives the problem is in PSpace, providing a tight upper-bound to the PSpace-hardness already established for turn-based games. In the case of Muller objective the problem is in ExpTime. We also obtain positive results when we assume a fixed number of agents, in which case the problem falls into PTime for reachability, safety, Büchi, and co-Büchi objectives.