This paper presents a novel parametric model that will be used to optimize the yaw settings of wind turbines in a wind plant for improved electrical energy production of the whole wind plant. The model predicts the effective steady-state flow velocities at each turbine, as well as the resulting electrical energy productions, as a function of the axial induction and the yaw angle of the different rotors. The model has a limited number of parameters that are estimated based on data. Moreover, it is shown how this model can be used to optimize the yaw settings using a game-theoretic approach. In a case study we demonstrate that our novel parametric model fits the data generated by a high-fidelity computational fluid dynamics model of a small wind plant, and that the data-driven yaw optimization control has great potential to increase the wind plant's electrical energy production.