I think you're missing the point, PAXboy, SIA and Thai already serve Munich, and presumably both have decent onward connections to Hong Kong.
The decision to match or undercut other carriers' fares will be a commercial one, with a lot of input coming from the airline's regional sales managers in (in this case) Germany and HK, who will have one eye on their sales targets and their load factors and the other eye on what their competitors are doing.
If they ask Head Office for a matching fare, Head Office may or may not take into account their competitive relionship with their alliance partner.