This thread is closed but as mentioned here:
Third place in single elimination tourneys goes to the person who lost to the eventual winner in the final.
However it seems to me that there is a case to have a play off between the two semi final losers. The match would take place in parallel to the final anyway and wouldn’t generally hold up the outcome of the tourney and the two players would not have previously met so it seems arbitrary to grant one of them the third place over the other.
An obvious possibility is that 2 dans meet in the final having played a DDK and an SDK in the semis. The DDK might end up with third place even though that is highly unlikely to be the outcome if there were a play off.