This article provides a possible explanation for the heterogeneity of tax reaction functions under tax competition. In particular, we assume the existence of three jurisdictions, i, j and z, as well as of spillovers. Given this simple framework, we show that if jurisdictions compete to attract mobile capital, spillovers can lead to asymmetric responses. In fact, jurisdiction i may react positively to a change in the tax rate of jurisdiction j and negatively to the change occurred in jurisdiction z. These findings are helpful to understand the mixed results of the empirical literature. Moreover, they have policy implications in that they explain the lack of tax convergence among jurisdictions. In particular, if at least some tax reaction functions have a negative slope, there are no symmetric equilibria, and the well-known tax-cut-cum-base-base-broadening policy would fail to hold.