Merkel and Shroeder

[Xiahou]

If no majority coalition can be formed, doesn't the president have the authority to name the party with a plurality as in charge?

[Leodegar]

If no majority coalition can be formed, doesn't the president have the authority to name the party with a plurality as in charge?

No. The president has only representive duties and no real power at all. A tribute to the Weimar Republic, when the Reichspresident used his power to establish Hitler as Chancellor...