mid-15c., apparently from Old French barater "to barter, cheat, deceive, haggle" (also, "to have sexual intercourse"), 12c., of uncertain origin, perhaps from a Celtic language (cf. Irish brath "treachery"). Connection between "trading" and "cheating" exists in several languages. Related: Bartered; bartering. The noun is first recorded 1590s, from the verb.
While one-to-one bartering is practiced between individuals and businesses on an informal basis, organized barter exchanges have developed to conduct third party bartering which helps overcome some of the limitations of barter. A barter exchange operates as a broker and bank in which each participating member has an account that is debited when purchases are made, and credited when sales are made.
It’s hard to answer that without actually seeing a modern gift economy in action. Luckily, modern gift economies actually do exist. On a small scale, they exist among friends, who might lend each other a vacuum or a cup of flour. There’s even an example of a gift economy on a much larger scale, albeit one that’s not always in operation: The Rainbow Gathering, an annual festival in which about 10,000 people gather for a month in the woods (it rotates among various national forests around the country each year) and agree not to bring any money. Groups of attendees set up “kitchens,” in which they prepare and serve food for thousands of people every day, all for free. Classical economists might guess that people would take advantage of such a system, but, sure enough, everyone is fed, and the people who don’t cook play music, set up trails, teach classes, gather firewood, and perform in plays, among other things.