But he hopes they will not create pressure to increase salaries in Wales.
There is an agreement which limits the regions bidding for each other's players, however Scarlets faced competition when re-signing centre Scott Williams who was out of contract at the end of the season.
"You've got to be realistic because it is a free market," Short said.
"No agreement can constrain someone's ability to look for work, and regions will be ambitious and will have their own player requirements.
"How the financial fallout from that works is part of the regions' agreement, and one would hope that you wouldn't see pressure within Wales to increase salaries because we've got enough to deal with outside of Wales."
Wales international Williams had been expected to renew his national dual contract (NDC), funded 60% by the Welsh Rugby Union (WRU).
However, the WRU withdrew their offer with union chairman Gareth Davies saying it was because the regions had "upped the ante".
Williams ended up signing a conventional deal with the Scarlets.
The NDCs were introduced as a mechanism to stop high-profile players leaving Wales for England and France.
Short was chairman of the regions' representative body - now called Pro Rugby Wales - when they negotiated the deal which funds and governs domestic rugby in Wales.
He said he would not have expected the union to get involved in a bidding war, and backed the dual contracts.
"The union have been excellent in supporting regions in the past year," he added.
"The NDCs are working well and everybody should recognise that it's a new concept and will take some time to settle down, but it is settling down well.
"And congratulations to the union - it's been a sea-change in the relationship over the past year or so."
Scarlets chairman Nigel Short admits it will be hard to stop regions competing against each other for Welsh players.