  In this paper, we investigate the rational synthesis problem for concurrent
game structure 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
technique as opposed to previous approaches that are logic based. Thanks to
this approach, we construct a zero-sum turn-based game that can be adapted to
each one of the afore mentioned objectives thus obtain new complexity results.
In particular, we show that reachability, safety, B\"uchi, and co-B\"uchi
conditions are PSpace-complete, Muller, Street, and Rabin are PSpace-hard and
in ExpTime.
