Q:

How can I change the resolution in Emergency 2014?

Emergency 2014 allows only to select screen resolutions in 4:3 ratios.
How can I set it to the native resolution of my monitor, 1920x1080?

A:

You can set the resolution by editing the configuration file. The file is located in %localappdata%\Quadriga Games\Emergency 2014 (just copy&paste this in the address bar of your Explorer window).
Open em2014.cfg with a text editor that can handle unix line breaks, e.g. Notepad++ or WordPad, it will not look pretty in the windows Notepad.
Edit these lines:
<var name="start_resolution_x" value="1920" />
<var name="start_resolution_y" value="1080" />

Save the file, launch the game.

