You've received a job offer. It pays more than your current job. But for whatever reason, you have decided that you would prefer to stay put. You have, however, made a decision to use the offer as a bargaining chip. It's a dangerous game, and you should only engage in it if you truly can see yourself walking away and accepting the new position. Many articles on the Web make it sound like accepting a counter offer to stay with your current employer is a kiss of death--but I'm not convinced.
