Many software-intensive systems consist of components that interact to fulfill complex functionality. Moreover, often many variants of such systems have to be designed at once. This adds complexity to the design task. Recently, we proposed a scenario-based approach to design product lines, which combines feature diagrams and Modal Sequence Diagrams. We proposed a consistency-checking technique based on a dedicated product line model checker. One limitation of this technique is that it is incomplete, i.e., it may fail to show the consistency of some consistent specifications. In this paper we propose a new game-based approach that overcomes this incompleteness and, in addition, automatically synthesizes controllers for the consistent product specifications. We exploit the fact that many variants are similar and efficiently synthesize product controllers incrementally. We provide a prototype tool and evaluate the efficiency of the approach.