Switzerland’s private banks have until Monday to decide whether to bow to US pressure and ditch the centuries-old culture of secrecy that has made the Alpine state a global vault for the world’s rich.

Many are leaving it to the last minute to tell the Swiss financial regulator whether they will participate in a US programme to settle tax evasion suspicions that could trigger large fines and force them to identify US customers suspected of using their Swiss accounts to dodge taxes.

Listed banks which participate in the programme could start telling investors from next week whether or not they have to take provisions against possible fines.

If they do not settle, individual banks and their senior staff risk criminal prosecution and, if a large number refuse to cooperate, it could hold up a future settlement for around a dozen of Switzerland's largest banks, including Credit Suisse, Julius Baer, Pictet, and local government-backed Zuercher Kantonalbank (ZKB).

Most of the 300 or so smaller banks are expected to participate but they are anxious to find out what others are doing and wrestling with the risk of giving up client confidentiality, which could put off customers. “Probably a few dozen will risk being pursued by the US later and stay out of the current programme altogether,” said a lawyer involved in bank talks.

Despite knowing the terms of the August deal for months, many banks are going down to the wire with their decision, according to several sources involved in the talks. US tax lawyers worked the Thanksgiving holiday for their Swiss bank clients and flew into the country this week as hundreds of boards gather to make their call. “It’s really an elaborate game theory going on right now,” said one US lawyer working for Swiss banks. “It’s a herd mentality.”

The US department of justice and Switzerland's financial regulator Finma declined to comment on how many banks had so far agreed to settle.