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As humans and robots start to collaborate in close proximity, robots are tasked to perceive, comprehend, and anticipate human partners' actions, which demands a predictive model to describe how humans collaborate with each other in joint actions. Previous studies either simplify the collaborative task as an optimal control problem between two agents or do not consider the learning process of humans during repeated interaction. This idyllic representation is thus not able to model human rationality and the learning process. In this paper, a bounded-rational and game-theoretical human cooperative model is developed to describe the cooperative behaviors of the human dyad. An experiment of a joint object pushing collaborative task was conducted with 30 human subjects using haptic interfaces in a virtual environment. The proposed model uses inverse optimal control (IOC) to model the reward parameters in the collaborative task. The collected data verified the accuracy of the predicted human trajectory generated from the bounded rational model excels the one with a fully rational model. We further provide insight from the conducted experiments about the effects of leadership on the performance of human collaboration.