Cognitive Daily

Suppose you’re playing a game where the goal is to accumulate as many points as possible. Now suppose your decisions — and only your decisions — control not only how many points you get, but also how many points the other player gets. Suppose further that at the end of the game, you’ll be able to cash in your points at a rate of 10 cents per point.

Now consider this scenario, one of a series of similar scenarios throughout the game: If you take 7 points, then the other player gets 9 points. If you take 5 points, then the other player gets 3 points. How many points would you take? Let’s make this a poll:

Now think about a different scenario, which I’ll present below.

This time, it’s not a game, it’s a one-time payout, but again you control the payouts. You choose between two options: You can get $500 and some other anonymous person will also get $500, or you get $600 but the anonymous person gets $800. Make your choice in the poll below:

This scenario isn’t much different from the first one, except that the payouts are bigger and it’s not described as a “game.” In both cases, the only way to maximize the amount of money you get is to ensure that someone else gets even more money than you. But if our poll responses match the results of a recent study, we should find a different result for each.

A 1992 study led by Max Bazerman asked the $500/$600 question to business students and accounting firm managers, and most respondents took the hypothetical $600, even though it meant they wouldn’t be getting as much as their imagined rival. Arguably this is the optimal response, since it maximizes the amount of money the respondent gets. Who cares if someone else gets more?

But if you think about this scenario as a game, more like our first poll, then the only way to “win” is to consistently take less money. If you’re asked to make a series of decisions like the 7/9 point — 5/3 point choice, if you choose 5 every time, at the end of the game you won’t have as much money as you would have made by choosing 7 every time, but at least you’ll have more than that other guy. But if the game has several rounds, there’s another option: you could alternate between choosing 5 and 7 points, and at the end of the game, you’d have the same amount of money as your opponent, so you wouldn’t “lose,” but you’d still make more money than choosing 5 every time.

Arthur Kennelly and Edmund Fantino presented this challenge to 200 college students with a couple extra twists: some students were told they were playing with a live human in an adjoining room, while some were playing against a computer. Some students were rewarded with real money — 7 cents per point — while others were given the same course credit for participation, no matter how many points they earned. Here are the results:

As you can see, respondents fell into three distinct categories. There was a large group of students who always took more points for themselves and another group who always took fewer points — and therefore more points than the other player. But there was also another group that chose more for themselves exactly half the time, thus matching the other player. So some people just want to maximize their total number of points, ignoring how much the other player gets. Others appear to be trying to match the other player’s score exactly, maximizing their own score while still not “losing.” Finally, others seem to be concerned only with “winning,” always choosing the smaller amount of points but always getting more points than the competition.

But when the responses were broken down according to who was being paid real money, the pattern changed dramatically:

If real money was at stake, just 3 out of 100 participants chose the smaller number of points every time. Most participants either went for the 50-50 option or always chose more points for themselves. But in the purely hypothetical game, where points couldn’t be cashed in, almost no one attempted to maximize their total points — they went for the win instead. This has very important consequences for researchers trying to save grant funds: people behave differently when they’re motivated by real money as opposed to hypothetical money or points. The low-budget experiment that doesn’t actually offer participants real rewards is not equivalent to one where the subjects are actually compensated based on their choices.

But there was no difference in the results when the students believed they were playing against a real person or a computer. Even though there was no interaction between the computer and the study participants, they still tried just as hard to “win” the game, especially when winning didn’t cost real money.

In a second experiment, Kennelly and Fantino changed one key element. Instead of referring to the choices as a “game” with “players,” they presented a new set of instructions about “scenarios” with “participants.” In this experiment, the results were very different. Regardless of whether real money was at stake, only 4 of 156 participants chose fewer points (and therefore more points than the other “participant”) every time. When real money was awarded, nearly all the students chose to optimize their personal reward, and when they were only playing hypothetically, nearly everyone chose to equalize the amounts they earned. Again, there was no difference between a computer and human “opponent.”

In Bazerman et al.’s 1992 study, a different result was found. Even with hypothetical money, participants chose to maximize their own earnings, rather than to equalize with a “competitor.” How can the two studies be reconciled? Obviously Bazerman’s team was using a very different scale of earnings: the maximum amount it was possible to earn in Kennelly and Fantino’s experiments was just over $10, while in the older study the reward could be as much as $600. It’s also possible that Bazerman’s business students had different attitudes about money than Kennelly and Fantino’s psych majors. In fact, our little demo may be able to shed some light on that issue. If our readers choose the $500/$500 split rather than the $600/$800 split, that suggests that the different participant pools explain the differences between the other studies. Otherwise, some other difference between the two studies is probably responsible.

Either way, it’s quite clear that the framing around these questions is almost as important as the questions themselves. Even when real money is involved, people will behave very differently depending on how they’re asked to choose how to divide money between themselves and others.

Kennelly, A., Fantino, E. (2007). The sharing game: Fairness in resource allocation as a function of incentive, gender, and recipient types. Judgment and Decision Making, 2(3), 204-216.

Comments

#1 qetzal
November 19, 2007

But if you think about this scenario as a game, more like our first poll, then the only way to “win” is to consistently take less money.

I don’t know about Bazerman’s study, but this isn’t how I interpreted your first poll. You said the goal was to accumulate as many points as possible. You didn’t say that winning required getting more points than anyone else.

I admit, describing it as a game made me feel like I should try to get more points than my ‘opponent,’ but since that wasn’t the stated goal, I resisted the temptation & picked option 1.
#2 Markk
November 19, 2007

I’m having trouble with the first scenario. What is “winning” in that game? I would make a deal with the opponent to split the money and always maximize value. If the opponent is an “enemy” then what you say are values are not true since there would supposedly be some value in neutralizing and giving less resources to the enemy – which means the values are wrong. The way you present it “winning” is meaningless. That to me is what is changing the data – you are missing what the winning represents – did students think they would get better credit for winning – even by implication? Something is missing.
#3 Kevin
November 19, 2007

I agree with the first poster. I at first thought you had to beat the other player but then when I reread you statement, “the goal is to accumulate as many points as possible,” I realized it does not matter how many points the other person gets. So taking 7 points over 5 points is always better as long as you are not in competition with the other player.

I did something like this under a fMRI machine for a neurology experiment. I was given up to 10 points to keep or to give to the other player. Those points I give the other player are multiplied by 4 and the other player gives me some back. The purpose was to get as many points as possible.
#4 Dave Munger
November 19, 2007

The study never suggested there was any criterion for “winning” the contest. It didn’t even say there *was* a contest. It simply described the scenario as a “game” and indicated how many points each “player” earned based on the participant’s choices.

The participants interpreted this as a competition, in which their goal was to earn more points than their competitor, not just to make as much money as possible.

The implication is that there’s a competitive urge, either innate or socially conditioned, that manifests itself in certain contexts but not others.
#5 Freiddie
November 19, 2007

I would consider poll #1 more indecisive for me than poll #2, since I’m as if I was tugged by two virtual forces of winning the game or getting more money, or something like that.
#6 Hao
November 19, 2007

I think the point about the difference in subject pools is important. I can imagine business students being trained not to make decisions that give their competitors an edge, even if it means sacrificing some personal benefit (the lesser-but-equal payout).

I’m also curious as to what the students were playing “against” and what kind of behavior the computer was programmed with, assuming at some point that they actually played with a computer.
#7 Mr. Gunn
November 19, 2007

Well, at the end, you still end up with more money picking the more lucrative option, so when you consider that the other person must know this too, there’s no question which one you should choose in either scenario. I imagine this is how a lot of venture funding gets distributed.

/technical note: COinS activators such as OCLC’s firefox extension replace the whole span with an icon or text link to the resolver, so best practices call for putting only machine readable stuff in the span, and the human readable citation outside.
//got your email, will follow-up soon
#8 Dread Polack
November 19, 2007

I’m an avid board-gamer. I even worked (briefly) for a large board-game company and regularly play with a professional designer. I think I might have come at this in a different way. The goal of a board game is to win, and there are very different ways of winning different games. Board games are often categorized as how competitive they are, and whether you’re simply trying to out-score your opponents or “screw” them in some way.

If I approached this as a competitive board-game, I’d choose whatever gave me the most points. That’s all that matters- whether you win by 1 or 100 points doesn’t matter. If I approached this as a money-making opportunity, then I’d go for whatever gave me the most money, and pay little attention to how much money the other person is getting. Assuming the anonymous other person is making no choices, they should be happy to get any amount of free money.

Of course, if I could in some way communicate with the other person, I’d propose a deal to split the difference, and then go for the most total money.

…and making deals with other players is another dimension to some board games, but that’s for another discussion
#9 Patrick
November 19, 2007

I think the most logical explanation for the differing results when using real money is the differing definitions of winning in the context of games and in the context of making money, as implied by Dave Munger. In the United States, “games” are most often competitive, and the “game” context is primed by awarding the participants points. In this case, the definition of “winning” becomes “getting more points than the other player”. However, we are generally taught to maximize our own individual payoffs when dealing with our own individual money, so the definition of “winning” becomes “getting as much money as I can”. I would venture to guess that casinos take advantage of a similar concept by forcing players to exchange their money for either chips or points in the case of slot machines – by doing so, they change the definition of “winning” from “getting as much money as I can” to “having fun”.
#10 Tony Jeremiah
November 19, 2007

This bares some resemblance to the Traveller’s Dilemma post sometime ago involving a combination of money and competition.
#11 Qalmlea
November 19, 2007

When I first looked at the question, as a game, I started to go for the 5/3 payout, but then I reread the description, where it just said “the goal is to accumulate as many points as possible.” That convinced me to change to the 7/9 option. Is this how it was worded in the other studies?
#12 Kevin Spring
November 19, 2007

I don’t know if business students would necessarily choose the lesser points if they thought they were in competition. I would hope that they understand a little about economics. Many economists go crazy when people do exactly as this study does. They can’t explain why people would choose lesser reward to hinder another person in non zero-sum games.
#13 Abby Normal
November 20, 2007

I’m also confused about the wording of the first question. You state the goal is to accumulate as many points as possible, not as many points as possible for yourself. So wouldn’t picking 7 and 9 accumulate 16 points, while picking 5 and 3 only accumulate 8 points? Therefore picking 7/9 would be the only way to achieve the goal.

I realize at least some of the participants took it to be a competition. But that question, as worded, seems to be testing something completely different that what’s discussed in the rest of the article. Or am I missing something?
#14 Who Cares
November 22, 2007

@kevin:
Think of comparative fitness for survival.
Accumulation of goods increases survival chances. Making sure rivals get less then you also increases your survival by reducing their chance at success.
@Qalmlea & Abby:
Read comment 4 about this being how the study was worded.
#15 Fred
December 11, 2007

Or, you could think of it as fitness for being a moron. Anyone can read the descriptions and see the exact criteria and know that they shouldn’t concern themselves with the other player. Amazing.