This paper proposes a new decision-making framework in the context of Human-Robot Collaboration (HRC). State-of-the-art techniques consider the HRC as an optimization problem in which the utility function, also called reward function, is defined to accomplish the task regardless of how well the interaction is performed. When the performance metrics are considered, they cannot be easily changed within the same framework. In contrast, our decision-making framework can easily handle the change of the performance metrics from one case scenario to another. Our method treats HRC as a constrained optimization problem where the utility function is split into two main parts. Firstly, a constraint defines how to accomplish the task. Secondly, a reward evaluates the performance of the collaboration, which is the only part that is modified when changing the performance metrics. It gives control over the way the interaction unfolds, and it also guarantees the adaptation of the robot actions to the human ones in real-time. In this paper, the decision-making process is based on Nash Equilibrium and perfect-information extensive form from game theory. It can deal with collaborative interactions considering different performance metrics such as optimizing the time to complete the task, considering the probability of human errors, etc. Simulations and a real experimental study on "an assembly task"-i.e., a game based on a construction kitillustrate the effectiveness of the proposed framework.