We give 50 cents per year of age. There's nothing wrong with SOME money being tied to work. We work for our income. But be sure that you separate "family work," which everyone does in order to contribute to the overall wellbeing and running of the home, and nobody gets paid for, and "extra work" they can do to earn extra spending money. In our home, memorizing bible verses is also a way to earn some extra money. Our boys go shovel driveways in the winter, and mow lawns in the summer, to earn extra money. We also live next to a golf course, so the boys go hunt for lost golf balls and sell them.
You can institute a demerit system along with their allowance, but beware: You have to keep track of it. I also don't believe in using allowance as a discipline tool when it doesn't fit the crime. If you're not getting along with your sibling or have a bad attitude, you address that specific issue (Fighting over a game? Put the game away and go play separately. Having a bad attitude? Go to bed an hour early because you're clearly tired and grumpy and need some time without an audience.) As tempting as it might be to take all their allowance, I don't think that, at 6 years old, it will fix their attitude, just make it worse. If there are anger issues, we have to work with our kids over time to be able to identify and manage their emotions. Taking their allowance does not teach them to do that.
Finally, be sure that you start smart by helping them understand that money should be budgeted. The easiest way to start is to talk about a percentage to be given (or tihe, if you are a Christian family), a percentage to be saved long term (we do 20% in their bank accounts), and then the rest for spending or saving short-term as they see fit. If they do decide to save some of their spending money for something special, sometimes kids have a hard time disciplining themselves enough to not dip into it. So we parents keep encouraging them and help them keep track of how much they have saved for their goal, and how much the have left to save to meet it. It helps instill that patience and discipline needed in order to stay the course...and that's a lesson that will last their entire lives.
Best of luck.
ETA: I just wanted to say, it's important that your kids' chores aren't just "their" stuff. I see parents all the time who only make their kids clean their own room and pick up after themselves, but mom and dad are constantly doing things to benefit the entire family. Nope. Kids need to pitch in on chores that help everyone too. You never want to hear, "But that's not even mine. Why should I have to do that?" You go grocery shopping for everyone, not just yourself, right? And pay for the electric bill for the entire house, not just the lights you turn on and the TV you watch. Kids need to know that it's not all about "I, me, mine," but that the entire family matters.