I applied for several postdoc positions recently. One made an offer which I accepted. Since then I've been invited for an interview for one of the other positions. Is there any benefit to attending? Is it an opportunity to make potentially useful contacts (in a relatively small field)? I should add that I have no experience with academic interviews (the position I secured was through contacts). Expenses will be paid.
Once you've accepted a job offer, you are supposed to inform other places that you've applied that you would like to withdraw from consideration.
If they still want to invite you over to give a talk knowing that you can not be considered for the position, go ahead. But, you must tell them.
To do otherwise would be a serious breach of ethics. You do not want to gain a reputation as someone who engages in unethical behavior (don't assume they won't find out).
Let me emphasize a point made in other answers.
As soon as you accepted one offer, you should have withdrawn your application from the other employers immediately. If you had done so, this situation would not have arisen.
You should immediately write an email to the school offering this interview, saying you have accepted another offer, and apologizing for not letting them know sooner. They have a right to be a little annoyed with you; you've wasted some of their time, and if they'd known you were off the market, they could have moved on to pursue other candidates.
So you made a mistake; well, people are human and these things happen, but you should act quickly to put it right.
In a comment on another answer, you consider the possibility of not telling them, and attending the interview anyway for the experience (and the free trip). Don't do that. In academia, attending an interview for a job you know you won't take would be considered extremely unprofessional and possibly unethical. Interviewing a candidate is expensive, in terms of time, money, and opportunity cost (time they spend interviewing you is time they don't spend interviewing candiates who might actually come; the longer they take to get to those candidates, the greater the chance they will take another job first). Don't think they won't find out; academia is a small world, people talk, and you can easily make enemies doing something like this. Moreover, the people at your chosen instituion can find out too (the other institution's colloquium schedule is probably public) and it won't make them think well of you.
In principle they could ask you to come anyway just to give the talk, but it's unlikely. They will probably want to use that time and money right now to speak with another candidate. It's quite possible they are still interested in hearing about your work, but they'd be more likely to invite you to visit sometime in the future, after job season.
You must inform them that you've accepted a position.
If they still invite you for a talk, you should go because presenting to new people will give you more visibility, more feedback on your work, and if you make a good impression then a potential place of employment in the future.
They might still invite you for a talk because it is fun for them to attend good talks and learn about interesting papers. Even if you don't work for them, by spending a day there you might meet someone interesting and you might wind up co-authoring with someone there on something in the future. Only good things can come out of spending a day with other researchers who are excited about stuff similar to yours.
< But why not take advantage of those benefits by not telling them I've already accepted a position?
The fact that you are asking that question after seeing the answers here, and acknowledging that it is "unfair" (actually it is dishonest), raises serious questions in my mind about your integrity and character. To be fair, you are possibly a young man who haven't quite made up your mind whether you are also going to be an honest one.
If you feel that you have something to gain by dishonesty, you're in a great deal of company (see Nick's answer, for example). You will always find those who applaud your dishonesty as willingness to make "tough decisions", "take on the grey areas", "get the job done" and so on, who all the while find ways to manipulate you in dishonest ways for their own perceived gain, and to your perceived loss. If you wish to be that sort of person, then you may expect to draw persons of like mind into your circle of acquaintances.
You will also find that honest people do not respect and trust you; you will furthermore find that dishonest people pretend to respect and trust everyone and actually respect and trust noone.
We are in a phase of existence where we as a society are deciding whether to base our actions on "survival of the fittest" or "the whole is greater than the sum of its parts." To not decide is to decide for the former. Cast your lot and reap as you sow.
You must tell them. You won't be postdoc for life. Put yourself in their shoes. Simply think if you didn't have this job. What would you have made of this behavior?
For reasons everyone has mentioned, you must let the second place know that you've accepted another offer. In addition once you have accepted that offer, you really must commit to it.
However, if this second place is truly amazing, you can inform them that (1) you've already accepted another offer and (2) would still be interested in giving a talk (as people have mentioned) and (3) would be interested in taking this position if it were deferred for a year, in the chance that they don't find a good candidate this year (this is rare for post docs but does happen on occasion, depending on the funding source). This assumes that your current job only has a 1 year commitment (many jobs these days are 1 year with a possible extra year of support). This is a huge long shot. They most likely will say no, unless they have no other qualified candidate. This is the only situation I could imagine it being ethical for you do do the interview (with their knowledge).
Going to the second interview:
Declining the second interview:
People usually recommend to "not to lose reputation", and therefore decline the second job interview, after you accepted a job offer already. This what I would do, too.
However: you only really got the job on the first day after the probation period.
Until then, anything can happen. They can cancel your application before you sign the contract (happens many times) for many reasons: budget cuts, change in management, change in priorities, etc. Or they decide during the probation period that they don't want you (happens also).
Therefore, I recommend not burning all your bridges! There are different ways of saying no - how about doing it in a way that shows professionalism, and keeps some doors open for you for the future.
I recommend the following:
Write a letter to the other employer saying that
You can also offer to keep in touch for professional reasons, and/or offer to forward their job announcement in your network. If it's a small field, and people are hard to get with the right expertise, they will appreciate it.
It happened to a friend of mine that during the probation period, it turned out that the position was not as advertised, and he quit. He re-contacted the previous parallel interview offering. The company was happy to call him in again - the original position was not available, but they offered him a similar one.
If you just simply say "No", they won't know that you would have been interested.
I personally don't see the harm. However, if that interview went well and you were to be offered the job, accepting it would obviously be a crappy thing to do.
But I don't see any issue in going for an interview, even with no intentions of accepting the role. Experience in interviews is really important. And on the plus side, you don't have to go in completely nervous because you've already got a job, so it'd be easy for you to sit back and relax!
The second interview: Of course you can't tell ahead of time if they will make you an offer, or if their offer would be one you would accept, but the question is, if the second interview resulted in a job offer, would you consider accepting their offer?
Perhaps for you, the second place is the place you'd rather work. Maybe it's the place you've always dreamed of working. If this is the case, you should go to the second interview, without telling them about the other position you have accepted, and see what comes of it.
In regards to the "second place", there is nothing wrong with that. In light of their offer to interview you, you are reconsidering your acceptance of the previous job offer. It is not a "wasted effort" on their part.
In regards to the "first place": If the second place offers you a position, and you accept it, you will have to tell the people at the first place that you have reconsidered their offer and have decided to accept another position. I can tell you that this should not shake them up too badly. I'm sure it's happened to them before.
They are free, and many places often do, continue interviews in spite of making an offer to you that you have accepted. You may not work out for them, or they might find someone "better" that they would rather have working for them. Unless there is some sort of "contractual obligation" that you have not described, if you were to go and work for them, they could replace you, and you could move on to another position, at any time.
On the other hand, if you really want to work at the first position, or if you feel you have some "social obligation" to proceed with the position at the "first place" due to your relationship with your "contacts" there, and wouldn't consider any offer the second place might make, you should tell the second place you have accepted another offer before the second interview so they could decide if they want to proceed. And they might... If for some reason, they really want you, they might feel they could woo you away from the other position with a great offer.