A good read on induction cooker and the effects of pan material used, app note(PDF) from ON Semiconductors.
Induction heating is a well established method of generating heat in metal goods and has been used for decades. The induction cooking market is well established, but little has been written regarding the properties and interactions of the induction coil when a pan is placed on it. It can be seen that any metal pan will have losses due to eddy currents; however, those losses are small compared to those in pans with magnetic properties.
The type of magnetic material does not have an appreciable impact on the losses; however, the losses increase with frequency for all pans. Pushing switching frequencies higher will reduce the cost of the coil, resonant capacitor, and increase the efficiency of the unit. As switching devices advance in switching speeds, frequencies for these types of cookers with also increase to take advantage of these improvements.