Three-way storm lantern doesn't work right - what's wrong? The lamp used to work near 3-way bulbs. I figured the...

The lamp used to work near 3-way bulbs. I figured the bulb must be moderately burned out so I brought a brand new one and installed it. Turning the switch make the lamp progress either on or bad, but never exhibits and difference in the height of light. It's other the same on-off-on-off sequence. Any impression what could be wrong and what to do about it?