The Greek Superleague introduced a play-off mini league in the 2007 - 2008 season1, where teams that finished in positions 2 to 5 in the regular season compete for better placement in European qualification. The current play-off system is:
In the play-off for Champions League, the four qualified teams play each other in a home and away round robin. However, they do not all start with 0 points. Instead, a weighting system applies to the teams' standing at the start of the play-off mini-league. The team finishing fifth in the Super League will start the play-off with 0 points. The fifth placed team's end of season tally of points is subtracted from the sum of the points that other teams have. This number is then divided by five and rounded to the nearest whole number of points, if necessary, to give the other teams the points with which they start the mini-league.
For the 2011 - 2012 season, second placed (regular season) Panathinaikos FC started the play-offs with four points, while tied third placed PAOK FC and Atromitos FC, and fifth placed AEK FC started with zero points, although Panathinaikos finished the regular season 16 points ahead of PAOK FC and Atromitos FC and 18 points ahead of AEK FC. It might seem unfair, however fairness was the widely reported goal of the playoffs, in an attempt to normalize European participation and give a better chance to teams from outside Attica to qualify, given the somewhat unhealthy dominance of Attica based teams in Greek football.
Teams managed to finish first in the playoffs and qualify for the Champions League albeit not finishing second in the regular season in 2007 - 2008, 2008 – 09, and 2009 - 2010. Obviously there is a strong financial incentive, as Danger Fourpence already mentioned, as it's a essentially a mini-league where 4 of the 5 strongest teams of the season compete and all matches are considered derbies.
An interesting side-effect is that it's quite easy to predict the points the teams will start the play-offs with two, three or even more matches before the end of the regular season. It has been reported in the local media that play-off participating teams chose to give their last games of the regular season with teams comprising of youths and non-starters, in order to keep their stars rested for the mini-league.
1 Superleague 2007-2008 championship invitation (in Greek, PDF)