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U are playing Chess here son and not Checkers..

You made an opening gambit ny turning in a resignation. They thought well enough of you to think wait a minute here...or they want to buy time as you would be leaving a hole in their production. Personally I would go and listen to their counter offer to see what they have to say. From that you can discern which of the above is the operative reason why they are making an offer. If they seem receptive you can selectively lay your cards out as to the rational of why you are leaving their fine company. There is something to be said for being honest in laying out the cards..That is is to see how receptive they are to you and your ideas and aspirations. Do they greet your honesty with open arms or are they evasive. Remember if you stay you have to be comfortable with the situation and it is only through letting them know what you think that you can find that answer. Then mostly likely I would go home and sleep on it, making sure that I talked it through with someone who has no dog in the hunt. Out of that discussion one might be surprised at what conclusions might pop out.

Personally my first impression for your initial post is that U already have made up your mind.