Little question, big consequenses: What would have happened if the Belgians (the Army, King Albert I and his government) had not escaped from Antwerp (6-7 October 1914). How would this change politics in occupied Belgium? Would Germany annex parts of Belgium. And what would happen to Belgian-Congo?
I whould guess Albert I whould stay king, but Flanders and Wallonia whould still be seperated (like Austria-Hungary 1867). The Germans whould annex Belgium east oft the river Meuse, but after the war to keep the neutral nations friendly. Congo would have to resupply the Germans in Tanganyika. What do you think?
As was already stated, the government would not necessarily capitulate if the King is captured and cuts a deal. The Government would not be captured because they made sure to get out and not get bottled up in Antwerp. Assuming somehow the Germans close the ring (i.e. actually using their Ersatz divisions to close the ring around the city instead of throwing them away in Lorraine) and lock in the Belgian army, militarily things get interesting in the aftermath.
Do the British manage to reinforce the Belgian first and get trapped also? If so then the Entente is short a large number of soldiers. If not then they are a major problem for the Germans trying to siege the city, which means some Belgians can make it out.
Either way if the Belgians are not around during the Race to the Sea than there is a large gap in the lines the British and French have to fill. I don't know if the British would be on the spot and blow the dykes as the Belgians did OTL, because if not then the Germans have a lot more land to try and flank the Entente.
Most likely without the Belgians the Germans actually breakthrough at Ypres with their reserve corps and the Entente lines north of the Somme fold. The BEF is going to be trashed if it can even escape, while French aren't going to be as bad off, but will be missing a lot of territory and civilians now trapped behind German lines, with much of the former being industrial/critical ports. The British will have to keep more troops at home to defend against the fact that the Germans are now at the Channel Ports and there is a major public panic. Not only that, but with their large numbers of losses they will have less troops to commit to the fighting in 1915 and later and will be of lower quality, as the cadres that OTL survived the fighting at Ypres won't exist.
Furthermore the Germans now have lots of mines (coal, iron) that won't be near the front lines and destroyed so as to deny them to the Entente as a means of sneaking under German defenses. They can use these mines as well as captures farmland for their own uses instead of destroying them for safety reasons.