Split or Steal?
Cooperative Behavior When the Stakes Are Large
Imagine that you are on TV, facing a jackpot of £100,000. You and your opponent are asked to choose between two alternatives:
- If you both choose "split", you split the jackpot and you both go home with £50,000.
- If one of you splits and one of you steals, whoever chooses "steal" goes home with £100,000, the other with nothing.
- If you both choose "steal", you both go home with nothing.
The Golden Balls episode in which two contestants, Sarah and Stephen, faced this £100,000 decision has become famous. It has been discussed on many blogs, for example on JOE.co.uk . One of their screenshots summarizes what happens quite succinctly:
Another of their screenshots shows that this a rather devastating moment for one of the contestants… and that, despite their artificial nature, game shows have a bit more “psychological realism” than most laboratory experiments.
The game that the contestants play is a variant of the well-known prisoner’s dilemma, sometimes called a “weak prisoner’s dilemma” because stealing weakly dominates splitting: if the other splits, you are better off stealing, otherwise you get 0 either way.
Over 288 episodes of the show have been aired. This large dataset allows us to study the determinants of cooperation for large and widely varying stakes (min £2.85, mean: £13K, max: £100K), in a diverse subject pool.
What do we find? Overall, 53 percent of the contestants decide to cooperate. This percentage is roughly in line with findings from laboratory experiments, where stakes are much smaller.
Choices in the show are largely insensitive to the size of the jackpot: contestants cooperate about 50 percent of the time, irrespective of whether they are playing for a couple of thousand or one hundred thousand pounds.
Striking, however, is the high degree of cooperation when the jackpot is relatively small: for amounts of several hundred pounds, 70 percent of the contestants choose to split.
This high rate of cooperation leads us to suspect that in the context of the game—in which a jackpot of ten thousand pounds is ‘normal’—sums of money that are normally viewed as ‘large’ are perceived as being relatively ‘small’.
The conclusion that players “think relatively” also follows more directly from another analysis. The jackpot is determined through a random draw. Prior to this random draw, a considerable amount of focus is placed on the maximum potential jackpot. During the show?s first seasons?when few or no episodes of Golden Balls had been broadcast at the time of recording and contestants were not yet able to accurately estimate what they should expect to win in the show?we find that the choices of contestants are strongly influenced by this value: the higher the maximum potential jackpot, the smaller the actual jackpot appears, and the greater the likelihood that players cooperate. Amounts perceived as negligible apparently are not worth stealing on TV.
For age and gender, we find that young men are less cooperative than young women, but this difference changes with age: men are more cooperative the older they are, and, from an age of about 46 onwards men are even more likely to split than women.
We also find evidence that people have a preference for reciprocity. Each episode starts with four contestants, and only two make it to the final via two voting rounds. (see here for a description of the earlier rounds of the show).
It sometimes happens that one of the finalists had unsuccessfully attempted to vote the other finalist of the show during the elimination rounds, and this is found to have a large impact on the decision to either ‘split’ or ‘steal’. The probability of someone choosing ?split? drops by as much as 21 (!) percentage points if she faces an opponent who has tried to vote her off.
In line with the large literature on lying aversion, we find that people who promise to split are 31(!) percentage points more likely to cooperate than those who do not make such a promise. Promises are the strongest predictor of what a person will do.
Rather surprisingly, we find no support for so-called conditional cooperative preferences, defined as a preference for matching the (expected) choice of the opponent: players neither condition on their opponent’s promises, nor on their opponent’s demographic characteristics. Apparently, either players cannot or do not forecast the behavior of their opponents, or they do not have conditionally cooperative preferences. Our evidence for reciprocity suggests that it is the former rather than the latter interpretation that underlies these results.
In short, the British TV game show Golden Balls allowed Martijn van den Assem, Richard Thaler, and myself to examine the determinants of cooperative behavior in a controlled environment with large sums of money at stake. The paper was published in Management Science in 2012. It is available on the Management Science website or in working paper format on SSRN .