How to choose a preposition

[tomvtr]

Is there a rule that determines when a particular preposition is used?

For example, in the following sentences: “for signing” versus “to signing” and “for playing” versus “to playing”.

He was disqualified for signing an incorrect scorecard.
The two countries are close to signing a peace agreement.
They criticized the team for playing too rough.
In addition to playing tennis during the week, I play football on the weekend.

Thank you!

[Alan]

Unfortunately the use of prepositions in English is notoriously irregular! You must learn on a case-by-case basis. A good dictionary should give guidance on this.