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Queen's famous ballad 'We are the champions' was voted as the world's favourite song, according to a poll sponsored by Sony in 2005. It has become an anthem for sporting victories and if you believe some researchers, it is the catchiest song in the history of popular music.

Yet I'm not here to discuss popular rock songs, though there's plenty to say about that. It is just an excuse to discuss the experimental equivalent of ‘We are the champions’. It is a research methodology as popular and catchy as Freddie Mercury's anthem and just like Queen's work, you've probably heard about it but it just never gathered much of your attention. It is the ‘Ultimatum Game’.

The ultimatum game was first presented to the research community in 1982 in an article entitled 'An Experimental Analysis of Ultimatum Bargaining'. The authors devised a scheme to study their subjects natural reactions and strategies for bargaining. The experiment has then been replicated hundreds of times, with interesting results that challenged the perception of economists.

The ‘Ultimatum Game’ is simple in its definition: it is a game where two people are bargaining on how to split a fixed amount of money, by following certain rules. The first player proposes how to divide the sum between the two players, and the second player can either accept or reject this proposal. If the second player rejects, neither player receives any money. If the second player accepts, the money is split according to the proposal. The game is only played once and no counter offers are allowed, hence the ‘ultimatum’ name.

When the experiment was devised, economic theory predicted that the second player would happily take any amount more than zero. Game theory was popular among economists at the time and they modelled that any normal, rational human being would gladly prefer to earn one dollar, than to earn zero dollars (remember that rejecting the offer meant that no one gets any reward). Interestingly, experimental evidence quickly refuted this argument, the most common offer during the first runs of the experiment clearly favoured an even split.

According to some of the researchers, the reaction among the economists after the first results of the ultimatum game arrived was usually ‘clearly these people are stupid’1. Why would anyone give away half the loot if the second player would clearly take any amount of free money? Actually, further studies confirmed that this response was far more common than economists had ever imagined. Not only is an even split the most common solution found in most cultures, it became noticeable that offers of less than 20% of the amount of money were often rejected: people were refusing free money.

Only in an isolated culture in the jungle did economic game theory triumph. The Machiguenga people of eastern Peru, with an almost non-existent economy, were one of the few ‘rational’ subjects in the world where economic theory held and low offers were gladly accepted. After the first awkward results of the ultimatum game, economists thought that very unequal allocations were rejected only because the amount of money was too low. So in theory, the absolute amount of cash involved was not enough to produce strategically optimal behaviour. You are rejecting free money because it is just a dollar, your pride wouldn't be so hurt if you were offered something around ten or fifteen bucks.

However, economists failed once again. The experiment was repeated on several occasions and this time the amount offered was substantial. Studies found that the higher the stakes, the closer the offers approach an even split. Even in a $100 game played in Indonesia2, $30 offers were turned down. To put things in perspective, $30 can be the equivalent of up to two week's wages in Indonesia.

Due to these controversial results, just like Queen’s famous ballad, the ultimatum game has been sung and repeated around the world countless times. The experiment, in many variations or 'covers', has been replicated using various different individuals and cultural backgrounds3: men and women, Asian and Israelians, children, autistic persons and individuals with exceptionally high IQ's among others. Almost every time the experiment is replicated, some cool statistical technique is used, ranging from non parametric tests to some interesting recent developments that involved Logistic Regression models aimed to predict the behaviour of the participants.

Ran Spiegler, author of ‘Bounded Rationality and Industrial Organization’, once described the ultimatum game as ‘by far the most intensely studied experimental game’. Rock stars tend to die young, but don't worry, the ultimatum game has been studied for more than three decades by now and is still going strong.



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