In the beginning, Kickstarter seemed primarily like a venue for upstart bands or small theater companies to raise a few thousand dollars to get projects off the ground. Over the past year, though, Kickstarter has played a surprising role in gathering increasingly astonishing amounts of money for increasingly well-known artists. In March 2012, the video-game auteur Tim Schafer sought $400,000 to make a new game but ended up with $3.36 million; in May, the musician Amanda Palmer set a goal of $100,000 to record a new album and raked in more than $1 million.

Along with a rise in the site’s public profile, the media narrative about Kickstarter has changed from one of astonishment (“So, people will just give you money?”) to one of skepticism (“All right, who’s getting hosed here?”) to the current uneasy middle ground — optimistic but ready to jettison the whole thing as soon as some opportunist abuses it to abscond with a bunch of cash. Kickstarter-financed projects that run into trouble or fail to materialize are often cited as a flaw in the model: to take only the two examples above, Schafer has documented for his backers that his project is on a pace to run over its budget, and Palmer, following her windfall, has faced criticism for soliciting free help from local musicians while on tour. The suggestion in both cases is that their Kickstarter contributors were somehow duped, like suckers who fell for a Nigerian e-mail scam.

The common thread in all of this coverage is that it typically uses the language and logic of simple supply and demand, regarding Kickstarter essentially as a meeting place for entrepreneurs and investors. Which is a big reason the site’s success seems so hard to explain. Kickstarter, like the box of Magic cards I was given, is baffling by the tenets of a self-serving marketplace. (“What’s in it for him?” was the question my mother was trying in vain to answer.) And if you allow for things like file-sharing — and many Kickstarter rewards and projects are the types of things that could be pirated, like games, albums or films — then it becomes fairly clear that pretty much none of the people donating have a purely economic incentive to participate at all. Why not just let everybody else finance this new album and download a torrent of it later?

But Kickstarter backers aren’t investors, and they aren’t looking for the project that will give them the greatest return on their money. Kickstarter does not function as a store (as its Web site goes to great pains to remind you), any more than PBS is “selling” you a tote bag in exchange for your donation. Kickstarter as a phenomenon is made much more comprehensible once you realize that it’s not following the logic of the free market; it’s following the logic of the gift.

In his book “Debt: The First 5,000 Years,” the anthropologist David Graeber examines our history of debt and money, concluding, in part, that humans do not naturally tend toward impersonal, reciprocal exchange. Instead, exchange usually develops in cultures first as a part of a larger social and cultural ritual. One of the most compelling cultures Graeber profiles is the Tiv of West Africa, who have very particular rules about exchange. For starters, they believe that bringing an economic transaction to full completion is essentially immoral, or at least frowned upon, because it implies that one party doesn’t want anything to do with the other in the future. If a Tiv man or woman gives you a gift, you are supposed to respond with another gift of slightly greater or lesser value. The outstanding debt between the two of you is a signal that your relationship is going to continue. To respond with a gift of equal value would be to say implicitly that you wish to even things out and draw your relationship to a close.