Sounds to me like someone in your party is playing on a Strict NAT type connection (or NAT Type 3). The NAT type is determined by your router, as well as every other device standing between you and your internet service provider -- modem, bridge, the whole nine yards!
You'll need to know how to access your router's system software to make any of the suggested changes to your network configuration. If you don't know how to do this, don't worry -- you can look up directions for your router model on the manufacturer's website, or by contacting their Support Team.
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