It’s
Wednesday and I’m on a short week for writing, so today we’re
headed back to the realm of experimental economics to discuss a game
that is similar to the Dictator Game – the Ultimatum Game!
How
to Play
The
Ultimatum Game is very similar to the Dictator Game. There are two
players. One is given a sum of money and is asked to propose an
amount to be given to the second player.
If you stop there, you have the Dictator Game, but the Ultimatum Game goes a step further – the second person can refuse the split, and, by doing so, make it so that neither player walks away with any money.
Generally speaking, the game is played with about the same amount of money as the Dictator Game – anywhere from $10 to $50 is traditional in developed countries. As with the Dictator Game, the predictions of classical expected utility theory are very clear – the person giving the offer will offer the smallest possible non-zero amount of money, while the second person will accept any amount of money that is greater than zero.
And, as with the Dictator Game, the Ultimatum Game unequivocally demonstrates that the concept of a rational, utility-maximizing individual is not one that applies to the average person.
Results
If you stop there, you have the Dictator Game, but the Ultimatum Game goes a step further – the second person can refuse the split, and, by doing so, make it so that neither player walks away with any money.
Generally speaking, the game is played with about the same amount of money as the Dictator Game – anywhere from $10 to $50 is traditional in developed countries. As with the Dictator Game, the predictions of classical expected utility theory are very clear – the person giving the offer will offer the smallest possible non-zero amount of money, while the second person will accept any amount of money that is greater than zero.
And, as with the Dictator Game, the Ultimatum Game unequivocally demonstrates that the concept of a rational, utility-maximizing individual is not one that applies to the average person.
Results
From
this meta-analysis of 35 separate studies – predicated almost
entirely on determining potential cultural influences on average
offer and acceptance rates, but still useful for the purposes of
getting an overview of results – we can glean a number of important
results pertaining to the game.
First of all, people tend to offer a lot more than the smallest possible amount – the mean ranges anywhere from 20% to 50% of the total amount. In America, the mean offer tends to be around 40% of the pot.
Secondly, people tend to reject offers that are below a certain threshold – anywhere from offers below 10% to offers below 40%. In America, people tend to reject offers that are below 20% with a fairly high frequency.
Neither of these results is even remotely close to what you would expect if you had drawn conclusions from expected utility theory.
More interesting, of course, is how variations on the base game change the results.
Variations
First of all, people tend to offer a lot more than the smallest possible amount – the mean ranges anywhere from 20% to 50% of the total amount. In America, the mean offer tends to be around 40% of the pot.
Secondly, people tend to reject offers that are below a certain threshold – anywhere from offers below 10% to offers below 40%. In America, people tend to reject offers that are below 20% with a fairly high frequency.
Neither of these results is even remotely close to what you would expect if you had drawn conclusions from expected utility theory.
More interesting, of course, is how variations on the base game change the results.
Variations
How
do you vary the game, then?
Well, as with the Dictator Game, you can do two things – you can change how the game is played, or you can change the group you are selecting your players from.
In the vein of the first, there are a handful of things that are quite interesting.
Increasing the size of the pot does not change the mean offer of the first player, but does have a profound impact on what offers the second player agrees to – that is, the second player tends to agree to low offers much more often.
Changing the way the game is played such that the second player has to decide at what point they would change from rejecting to accepting an offer from the first player tends to slightly increase the ‘mean’ acceptance rate, largely, from what I can tell, as a result of being more accurate.
As with the Dictator Game, painting the first player as having earned the money lowers offers and raises acceptance rates, while painting the second player as deserving has the opposite effect.
For the second sort of variation, the Ultimatum Game is a little different from the Dictator Game – unlike the Dictator Game, which has a tradition of being played almost entirely in developed nations and the variations being largely in terms of inner-society demographics, the Ultimatum Game has been widely used by anthropological economists to study the differences between cultures.
As an example, the indigenous people of South America tend to accept offers of any amount and make offers that average around 15%, while some indigenous populations of the Malaysian and Polynesian island groups will make average offers of well above 50% that are routinely refused as a result of the incredible social implications of giving and accepting gifts of any kind.
Generally speaking, there can be a lot of differences here, but the majority of cultures tend to make average offers between 20% and 50% and will, on average, reject offers that are below about 15%.
Of all potential future variations, the one I’d like to see most is the same as my choice for the Dictator Game – a series of games in which the ‘randomness’ of who is the first player is varied between plays in such a way as to allow a serious examination of how this changes the mean offer and rejection amounts.
Well, as with the Dictator Game, you can do two things – you can change how the game is played, or you can change the group you are selecting your players from.
In the vein of the first, there are a handful of things that are quite interesting.
Increasing the size of the pot does not change the mean offer of the first player, but does have a profound impact on what offers the second player agrees to – that is, the second player tends to agree to low offers much more often.
Changing the way the game is played such that the second player has to decide at what point they would change from rejecting to accepting an offer from the first player tends to slightly increase the ‘mean’ acceptance rate, largely, from what I can tell, as a result of being more accurate.
As with the Dictator Game, painting the first player as having earned the money lowers offers and raises acceptance rates, while painting the second player as deserving has the opposite effect.
For the second sort of variation, the Ultimatum Game is a little different from the Dictator Game – unlike the Dictator Game, which has a tradition of being played almost entirely in developed nations and the variations being largely in terms of inner-society demographics, the Ultimatum Game has been widely used by anthropological economists to study the differences between cultures.
As an example, the indigenous people of South America tend to accept offers of any amount and make offers that average around 15%, while some indigenous populations of the Malaysian and Polynesian island groups will make average offers of well above 50% that are routinely refused as a result of the incredible social implications of giving and accepting gifts of any kind.
Generally speaking, there can be a lot of differences here, but the majority of cultures tend to make average offers between 20% and 50% and will, on average, reject offers that are below about 15%.
Of all potential future variations, the one I’d like to see most is the same as my choice for the Dictator Game – a series of games in which the ‘randomness’ of who is the first player is varied between plays in such a way as to allow a serious examination of how this changes the mean offer and rejection amounts.
Explanations
Unfortunately,
the Ultimatum Game shares too much with the Dictator Game for me to
treat an explanation of its results as particularly different –
both involve two players, both involve the distribution of randomly
distributed income, and both are played with real money.
As such, I would say a large part of the results from the Ultimatum Game come from the same source as the Dictator Game – that is, that people have an innate sense as to how randomly distributed income should be distributed between people, and that this sense, however it may be instilled, is the reason why individuals offer more than the lowest possible amount of money to the other player.
There is, however, a difference with the Ultimatum Game’s results that is important to note – that of why people reject offers.
In the literature, rejecting offers is often chalked up to a desire to punish the other player for iniquitous offers. While this probably covers some portion of the reason, I would put forth two other important motivations that should be considered.
First of all, pure self-interest is obviously important – and also noted in the literature, often as a countermanding influence to the desire to punish the other player. This motivation shows itself most in the decrease in rejection rate when the amount of money in the pot increases.
As such, I would say a large part of the results from the Ultimatum Game come from the same source as the Dictator Game – that is, that people have an innate sense as to how randomly distributed income should be distributed between people, and that this sense, however it may be instilled, is the reason why individuals offer more than the lowest possible amount of money to the other player.
There is, however, a difference with the Ultimatum Game’s results that is important to note – that of why people reject offers.
In the literature, rejecting offers is often chalked up to a desire to punish the other player for iniquitous offers. While this probably covers some portion of the reason, I would put forth two other important motivations that should be considered.
First of all, pure self-interest is obviously important – and also noted in the literature, often as a countermanding influence to the desire to punish the other player. This motivation shows itself most in the decrease in rejection rate when the amount of money in the pot increases.
Secondly,
it has been shown many times over that the utility gained from money
is relative as much as it is absolute – that is, it is based on the
wealth of those around you. As such, if you have more money than
anyone else around you, the utility you gain from the possession of
that money is much greater than if you had the same purchasing power
in another society but were at the bottom of the pack in terms of
overall wealth.
Adding the three together, the interplay between the desire to punish iniquitous offers, the desire to gain money for oneself, and the desire to keep the gap between yourself and the other player as narrow as possible probably covers the entire gamut of reasons for rejecting an offer.
And there you have it: the Ultimatum Game. As it is so close the Dictator Game, I chose to examine it second. As both belong to the same class of game – in my opinion, at least – I have held off on examining the policy implications of the games the game results. That will be covered next week, and then we will move onto other games – probably the Trust Game, but I have yet to make any real decisions there.
Adding the three together, the interplay between the desire to punish iniquitous offers, the desire to gain money for oneself, and the desire to keep the gap between yourself and the other player as narrow as possible probably covers the entire gamut of reasons for rejecting an offer.
And there you have it: the Ultimatum Game. As it is so close the Dictator Game, I chose to examine it second. As both belong to the same class of game – in my opinion, at least – I have held off on examining the policy implications of the games the game results. That will be covered next week, and then we will move onto other games – probably the Trust Game, but I have yet to make any real decisions there.
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