Help out a Newbie. About Tech Trading and research...

None, in this case. Some techs give you overall ability bonuses though, so they can be worthwhile getting if you skipped them previously.

Yes.

I'm not sure why (or if) an AI might accept Phasors II in exchange for IV, but you can always fill out your tech tree through research or futher trades.

Sometimes it can be helpful to have earlier forms of a tech when you're making ship design decisions like tradeoffs between space, power, and cost.

Hello. I was the one trying to trade for the lower tech. My reason was for tech stealing during invasions.

I hadn't done any research on the Phasor line. I had stolen Phasors, Phasors III, Phasors IV and Phasors V from invading planets. I wanted to trade for Phasors II, so that on the next turn when I invaded more planets I didn't steal a (to me) worthless lower level tech, I wanted to keep stealing my enemies highest level techs.

The AI wouldn't trade, and of course, in the next turn when I invaded worlds, I stole Phasors II, which was what I was hoping to avoid.

The AI I was trying to trade with was not the one I was invading. Both civs just had research done on that line.

There is at least one more possible reason. You might be trying to improve the tech of the AI you are trading with. If it doesn't have cash, you might as well try to fill your tech tree.

Oh, I was trying to improve the AIs tech. It was fighting a war I wanted it to win, and its ships were underpowered. Would have been a great way to kill two birds if it had accepted the trade.

The question in the original post was why would I (the player) want lower level techs.

Thank you all for answering. Now that you have explained it to me it makes absolutely sense

Thanks!