To run a company, employers need to hire people to realize a product, a sport coach can motivate some players intend to win a match, a designer have to force synchronization of some parallel processes to avoid deadlocking. In these examples, a device external to the global system tries to force the behavior of some agents, aiming at achieving a global objective. For realism purposes, we assume that forming a coalition has a cost that should be minimal. This cost models the fact that individuals of the coalition may be deviated from their original objective. Game theory is a vast field that addresses this kind of problem. In this work we focus on turn-based games, a simple and broadly explored branch of game theory. Turn-based games offer well-known tools, among which the most famous minmax algorithm where a constrained optimization problem is addressed [19]. The problem we aim at solving is to find a minimal cost coalition which enforces some position in a given set (the goal) to be eventually reached.