We investigate this issue in idealized experiments performed with the global climate model Planet Simulator (PlaSim). The model includes a prescribed SST and adopts a spectral resolution of T170 for resolving tropical cyclones. An idealized land-sea configuration with two oceans and two continents has been used to reveal the nonlocality mechanism. The model run starts with a spin-up phase of 10 years at a lower spectral resolution of T42 so that a steady climate can develop. Afterwards, the model runs for another year at the higher resolution T170. The tropical cyclone activity in the control run is similar in all four ocean basins (north-western, south-western, north eastern and south-eastern basin). Adding a positive SST anomaly of 2.5K in the north-eastern basin leads to a striking local increase of tropical cyclone activity measured in terms of the ACE index. However, the ACE index decreases in the other three ocean basins. The response is vice versa when a negative SST anomaly of 2.5K is added. Interestingly, the average ACE index rises in both perturbed runs. Therefore, it depends nonlinearly on relative SST yielding no global compensation of ACE index changes by positive and negative relative SST anomalies. Analysis of the planetary circulation reveals a divergent (convergent) flow anomaly in the upper troposphere over the warmed (cooled) ocean basin and a convergent (divergent) flow anomaly over the other basins. These anomalies change the distributions of convective available potential energy (CAPE) and low level vorticity in such a way that they support the simulated nonlocality of tropical cyclone activity. In aquaplanet simulations we found that the sensitivity of tropical cyclone activity to global changes in SST is smaller than due to a local change in one basin. These results suggest that it is of importance whether SST increases uniformly or inhomogeneously as a result of global warming.