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For the following setup:

         A   ----(HIGH Fee rate) ----  B  ----------------  C

B want to charge A for more fee, he raises the fee of the channel between AB

  1. A pays to C
  2. A pays to B
  3. C pays to A

Does high fee rate only affects case 1 only??

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No, only the third case is affected. And the reason for that is that channels are actually bi-directional and have two fee policies depending on the direction they are used.

For example, channel AB has a policy from node A, and a policy from node B. If B increases the fee - it will only affect the payments going from B to A, not the other way around.

That means that scenario 2 in your case is always controlled only by node A. Scenario 3 includes the payment from B to A, so fees will be higher. Scenario 1 can also be affected by node B, but it will need to increase fees on the channel BC, not AB.

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