multiple job offers issue

Finally got an offer from company X and I have signed the offer letter. Interestingly enough I probably will have a better offer from company Y in the very near future, around the start date of the 1st one.


Now there are a few scenarios.


1. If the 2nd offer is given before the start date of the 1st one, can I decline the 1st one?


If yes, isn't the company x screwed? What is the point for the future employee to sign the offer letter?


If no, then why? The offer letter states that "you are at will employee", which means your employment may be terminated by you, with or without cause.



2. If the 2nd offer is given after the start date of the 1st one, what is the consequence to resign a few days right after the start date?


BTW, I am US citizen right now, I don't need any sponsorship for employment via.


Could anyone shed some light on this issue?