Given red and blue points drawn from Poisson point processes of equal intensities, we match them by locally minimizing a cost function. We identify all possible measurable cost functions on R^d such that the resulting matching is scale invariant. Our cost functions can be asymmetrical, which we refer to as unbalanced cost functions. The investigation is motivated by a paper by Holroyd, Janson and Wästlund, where the authors consider scale invariant cost functions with some additional regularity assumptions. Furthermore, we discuss how different the unbalanced matchings are compared to these more regular cost functions for matchings between Poisson point processes on R.