The ultimatum game

Here's more following from Priceless, the book I'm reading by William Poundstone.

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An oft-repeated experiment showing that rational self-interest can be a poor predictor of human behavior is the ultimatum game. In this game, there are two players. The first player is given some money and must split it between himself and the other player. The second player then decides either to accept the first player's offer, in which case both players keep their allotted portion, or else the second player rejects the deal and both players get nothing.

For example, suppose the purse to be split is $10. The first player decides to keep $7 for himself and offer $3 to the second player. If the second player accepts the deal then the first player gets $7 and the second player gets $3. Else, if the second player rejects the deal, then both players get $0.

If both players are rationally self-interested—that is, if each player wants to obtain as much money as possible—then the first player will keep most of the purse for himself, and the second player will accept any nonzero offer. So an example of a rational split of a $10 purse might be, say, $9 for the first player and $1 for the second player. And both players would feel happy with the result, for each player got something out of the deal. But this isn't what usually happens when real people play the game. What often happens is the first player makes an even or near-even split—e.g., $5 to each player—or else the first player makes a heavily uneven split—e.g., $9 to the first player and $1 to the second—and the second player rejects the deal, turning away free money.

These results have held up across a multitude of variations of the game, including one variant where the two players never meet each other and remain anonymous and another variant where the players' roles as either first or second player are deservingly decided through a skillful challenge, such as answering a trivia question. Even so, players tend to turn down free money. What's going on?

One theory is that the ultimatum game as played in the laboratory is skewed by small purses, where small monetary amounts collide with players' sense of fairness. As a first player, even if you could get away with a $7/$3 split, you might feel guilty for doing so and would instead offer an even split. Or as a second player, you might find that $3 isn't worth the feeling that you were taken advantage of, so you might reject it. But what if you played with a $100 million purse? Would you, as the second player, reject a measly 1% offer of $1 million for pride? Unfortunately, no grants for playing with such large sums have been made available to psychologists to study the problem.

However, according to the Wikipedia article for the ultimatum game, the game has been played in Indonesia with a purse size equivalent to two months' average income for the country—that would be analogous to $7,000 in the USA—and the results were similar to what goes on with small sums. Many of the offers were even splits or near-even splits, and of the heavily uneven offers, many were rejected by the second player, despite that player having turned down several weeks' worth of income to do so. If the ultimatum game is skewed by a sense of fairness then fairness is worth more than just a few dollars.