She played for Czech Republic at the Women's Chess Olympiads of 1994, 1996, 1998, 2000, 2002 and at the Mitropa Cup in 1997. Ptáčníková has represented Iceland at the Women's Chess Olympiad in 2004, 2006, 2008, 2010, 2012, 2014 and the Women's European Team Chess Championship in 2005 and 2013.