An electronic ballast for a high-pressure discharge lamp includes a power converter and a controller. In the power converter, the input DC voltage is converted into a ballast output power for lighting an HID lamp and applied to the HID lamp. The controller has a function to control the power converter and change the ballast output power. The ballast has power modification means. The lamp power modification means detects a lamp output parameter indicated after the HID lamp starts discharge, identifies a nominal lamp power of the HID lamp according to the output parameter, and gives an identification signal indicating the identified nominal lamp power. In response to this identification signal, the power converter outputs a ballast output power matched with the nominal lamp power identified by the controller. <IMAGE>