Kitten Biting, Playing ?? Should I allow

Hello, I have a 3 month old female, Abby. She is full of energy. I love playing with her this way she leaves our 14 year old cat alone, well, not all the time.
She likes to attack my hand, leg or arm, and bite...not hard enough to break the skin,, just hard enough so I feel it. She kicks my arm with her claws in...
I probably promote this attack by moving my fingers, then I hold her with my hand like we are play fighting.... no one gets hurt.
Sometime she will use her front claws to grab me... but there is nothing to it.
My question is... should I deter this behavior, or will it stop on its own. I do not want her biting company when she grows up.
If I have to stop this behavior.. how do I stop it...

Unfortunately, it won't stop...you have to stop it . When I play with my kittens like that, I wear a thick glove (have had a couple of singletons who just needed to wrestle ). No glove, no wrestle. Also, try playing with more interactive toys- stick and string type toys (put these up when you're not there), laser pointer (don't point in her eyes!), jingle ball,etc. or get a stuffed animal to wrestle with, with her. Since she is already 3 months, I would suggest the stuffy would be the better option.

If she "attacks" you without the glove (or attacks you instead of the "stuffy"), timeout (like in a bathroom) for a few minutes, and then get her out with a distraction of another toy. If she goes after you again, timeout again, etc.

If she persists, ignore her and put your hands (or whatever body parts she is attacking) where she can't get them, then get out a toy when you have time to play. Make sure it's later, though, so she doesn't associate attacking your hands with you getting out the toy.

Also, growling or hissing when she is doing something undesirable always worked with my kittens- the shock on their faces when they realized it was me "saying that" was priceless! It still works today (my oldest is 14, youngest, 7).

Good luck!

It is probably me that causes the behavior.. but I may have started a bad habit. I will take your suggestion and slowly stop the biting. I do not want to do it immediate, since I caused the habit... but as you state, I have to stop it...We have pleanty of other toys we can play with... I just liked the personal interaction because I miss the love I had with another that passes away.

I had the same problem with my newest kitten when i first got her. However, slowly she learned the difference between playing and when it was wrong. Keeping a sheet or sock between the two of you is helpful. She is now several months old and knows the difference, and licks the spot she has bitten of scratched when she was not supposed to.