There's definitely something missing from the description of the experiment. It sounds like the first half of the http://en.wikipedia.org/wiki/Ultimatum_game. The second half—informing the player that their hypothetical "anonymous partner" would get to decide whether both, or neither, of them got the money—provides the incentive for the player to cooperate. Selfishness could then be gauged by how often players still choose "unfair" splits despite the chance of rejection.
If this is what the experiment was, though, I would question their methodology a bit; an important part of the Ultimatum game is that both partners have to think of one another as human—and therefore capable of irrationality. The partner anonymity in their experimental set-up creates (mental) distance between the partners, which encourages a more rational cost-benefit analysis, vs. the immediate "I should punish you for giving me such a bad deal" reaction you have to a real person. If the players realize this, they will benefit by acting more selfishly, because they can rely on their partner to not see them as "human enough" to be worth punishing.
If this is what the experiment was, though, I would question their methodology a bit; an important part of the Ultimatum game is that both partners have to think of one another as human—and therefore capable of irrationality. The partner anonymity in their experimental set-up creates (mental) distance between the partners, which encourages a more rational cost-benefit analysis, vs. the immediate "I should punish you for giving me such a bad deal" reaction you have to a real person. If the players realize this, they will benefit by acting more selfishly, because they can rely on their partner to not see them as "human enough" to be worth punishing.