The so called AA practise is a out coming foreign custom,origin in Holand.Out of his canniness and a typical of setting everything clearly,Dutch are prefer to pay for their own bills after a meal in eateries,which is what the AA originally means.Well it is quite different from the AA we have,the kind AA practise we have means that shareing the bills on average,this should be called more like "share equally" than AA practise.
And there is another saying,AA is short for acting appointment in English.The daylong busy Italian and Dutch businessmen have came to form their own special way of communication namely:talk when gather and apart paying his own bills.You know the businessmen are always travelling around and seldom stay at one place for too long due to the character of career.So when a person offer a treat to another,the guest always share the fees because there is a high possiblity that they would never meet again.That means the guest would never have a chance to treat back.Well also the characters of canniness and the typical of setting everything sorted of Dutchman gradually forms the idiom of "Let's go dutch".And the facetious Americans explain that by AA.