We present a model where heterogeneous districts choose both whether to experiment and the policies to experiment with. Since districts learn from each other, the first-best requires that policy experiments converge so that innovations are useful also for neighbors. However, the equilibrium implies the reverse - policy divergence - since each district uses its policy choice to discourage free-riding. We then study a clumsy central government that harmonizes final policy choices. This progressive concentration of power induces a policy tournament that can increase the incentive to experiment and encourage policy convergence. We derive the best political regime as well as the optimal levels of heterogeneity, transparency, prizes, and intellectual property rights.