How is an exchange of control handled when both permanents are controlled by the same player?

When an exchange of control occurs and both permanents involved are controlled by the same player, nothing happens because there is no actual change in control. For an exchange of control effect to have meaning, each player must control a permanent that differs from the other, allowing a switch that reflects a change in the game state.

In this scenario, since the same player controls both permanents, there is no transfer of control to another player, and the exchange effect effectively has no impact. The permanent remains under the same player's control, maintaining the original game state.

Other options imply changes, such as losing control or nullification of outcomes, which would suggest a modification in the state of the game that is not possible without distinct control between different players. The rules clearly state that control exchanges hinge on different players being involved; without that, the effect becomes moot.