Behavioral Economics is a relatively new discipline of economics that, rather than relying on complex mathematical models, instead takes the approach of sociology or anthropology by being grounded in research involving direct observation of how people behave - either in real life or in constructed 'games'. Its relevance to the gift economy is that a series of experiments have shown how far the economists' assumption of Homo economicus is from the truth. People are by no means as amoral, selfish and calculatingly rational as economists have been suggesting.
The dictator game is a perhaps the simplest behavioral economics (in fact it is so simple that is technically doesn't qualify as a 'game'). One player is given a certain amount of money and split it between himself and the second, entirely passive, player. Contrary to classical economists' assumptions that people always give as little as possible, many people often split the windfall 50:50. One approach to this is to lament people's lack of intrinsic selfishness, and to try to teach them to be 'economically literate', another would be to acknowledge that Homo economicus is a fatally flawed model.
The ultimatum game, based on the dictator game, is another demonstration of how people deviate from economists' expectation of selfishness. The first stage is like the dictator game, but player 2 has a choice either to accept the allocation (both players receive the money as split by player 1) or to reject it entirely (neither player gets anything). Typical behavior is for player 1 to split the money roughly equally, and for player 2 to reject uneven allocations.