No, trade goods are handled as an exclusive item that gives empire bonuses to those who own them. If you build a trade good, you may keep it for yourself, or sell/trade it to another empire (you retain it's bonuses, but they gain them as well, you can only sell it to an empire once, but you may sell it to any or all of the empires). If someone else builds the trade good first, you may purchase it from them.
When I said trade empires, I meant something else. You can build trade ships that estabish a trade route between two worlds. What this does is provide extra money to both planets (yours and someone elses). In one game I had built a trade empire where the trade routes I made were providing a significant source of income to eac of the major empires. This gave me great protection since people did not want to go to war with me (thus canceling the trade route, and cutting off thier much wanted income). Further, if my empire were to go to war, it would threaten the trade going to other empires (since traders are often targeted), and so other empires who also wanted the money would defend me (thus protecting thier own economic intreasts). I won the game without ever having to fire a single shot.
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