
willig
willing
Ready to do something without resistance or hesitation.
Er hat willig zugestimmt, bei den Vorbereitungen zu helfen.
He willingly agreed to help with the preparations.
willing / compliant
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willing
Ready to do something without resistance or hesitation.
Er hat willig zugestimmt, bei den Vorbereitungen zu helfen.
He willingly agreed to help with the preparations.

compliant
Easily submitting or yielding, often with the connotation of being easily influenced or obedient.
Der Diktator verlangte von seinen Untertanen willigen Gehorsam.
The dictator demanded compliant obedience from his subjects.
The adjective 'willig' (willing/compliant) is closely related to the noun 'der Wille' (the will) and the verb 'wollen' (to want). It describes a person who has the will to do something and therefore acts willingly.
Der Student war ein williger Teilnehmer an der Diskussion.
The student was a willing participant in the discussion.
In the meaning of 'bereit sein' (to be willing/ready), 'willig' (willing) is often used in the construction 'willig sein, etwas zu tun' (to be willing to do something). This is followed by a subordinate clause with 'zu' and the infinitive.
Sie war willig, die zusätzliche Arbeit ohne Bezahlung zu übernehmen.
She was willing to take on the additional work without pay.
In the meaning of 'gefügig' (compliant), 'willig' (compliant) is often used in the fixed expression 'ein williges Opfer' (a willing victim). This describes a person who can easily be persuaded or manipulated into something.
Er wurde ein williges Opfer ihrer Pläne.
He became a willing victim of her plans.
ready
Bereit and willig can both mean that someone wants to take on a task. Bereit can additionally leave open practical preparation or immediate readiness for action, while willig particularly emphasizes the absence of inner resistance. Use bereit for general willingness and willig when going along without objection is important.

Lea war willig, die schwierige Aufgabe ohne Widerstand zu übernehmen.
Lea was willing to take on the difficult task without resistance.
Nach der Vorbereitung ist Lea bereit, die schwierige Aufgabe zu übernehmen.
After preparing, Lea is ready to take on the difficult task.