In France, there are 70,000 consoles available, and just 20,000 of them will be sold over the counter outside the pre-pay advance booking system.
The launch of the 128-bit consoles with built-in DVD players had already been delayed because of a shortage of supplies - especially computer chips - at Sony's only PS2 factory near Tokyo.
In the UK, shoppers have been promised 165,000 consoles - down from the original quota of 200,000 machines. They are to be sold for £300 each.
Friday also sees the launch of PS2 in the Middle East, Africa and Australasia.
Bottlenecks
In other European countries, video game enthusiasts face similar bottlenecks.
In France, there are 70,000 consoles available, and just 20,000 of them will be sold over the counter outside the pre-pay advance booking system.
There a playstation will cost 2,990 Francs or 455 euros.
Chris Deering, the man in charge of Sony Computer Europe, said: "We would not have delayed the launch in Europe for a month, which cost us a lot of money, if we had had the quantities we requested from Tokyo".
Slow roll-out
According to industry analysts, Europe is the world's largest market for games consoles, but it is the last major market to get delivery of Playstation 2.
And it is also being priced considerably higher in Europe than in either the United States or Japan.
Its predecessor, the first Playstation, has been particularly popular in the UK and Ireland, where respectively 23% and 31% of all homes own a Sony console.
Sony launched PS2 first in the company's home market, Japan, in March this year. In less than four weeks, the company sold 1.4m PS2s. By October, it had sold more than 3.5m units.
In North America, Playstation 2 was launched at the end of October, amidst a midnight shopping frenzy. In just one weekend, ecstatic Playstation fans carried home 500,000 PS2 consoles.
Rivals
Playstation 2's main competitor right now is Sega's Dreamcast machine.
Unlike the Dreamcast, PS2 has no internet connection, although it is promised to be added in 2001 or 2002, once broadband web access is widely available.
But Sony's console has a DVD player, which could potentially turn it into the core of a home entertainment system.
Sony's arch rival, Nintendo, is not expected to launch its next-generation console before late next year.
The big unknown is a new entrant to the field, Microsoft. The company has announced plans for its very own games machine, the X box.
During this holiday season, Dreamcast and Playstation can dominate the market, although Sony is handicapped by its production problems.
But next year could turn out to be crucial for the outcome of the games console wars, once Nintendo finally delivers its long delayed 128-bit machine, and mighty Microsoft shows the strength of its hand.
For Sony and its rivals, a lot is at stake. Revenues from Playstation sales are already accounting for 28% of the company's net profits.