Let’s play a game.  Imagine that I give you 10 pound coins.  You have to share the coins with a stranger.  You are allowed to make just one offer.  So, for example, you might offer to keep four of the coins for yourself and give them six.  If they accept your offer then you both get to keep the number of coins being offered.  If the stranger rejects your offer then the entire deal is off and you both get nothing.  How many coins would you offer to keep for yourself?  Men vote in one poll, women in another…

1. Bryce says:

Well, my answer depends on whether or not the other person knows we both get nothing if they reject the offer. If they don’t know, I’ll be conservative. If they do know, I’ll be risky.

2. Richard says:

In addition does the stranger know how many coins you were given?

3. monxas says:

Do they know the hole deal? do they know what happens in each case? do they know how many coins there are? if they are not aware can i tell them? if i can tell them, can i tell them whatever i want? or only the truth…

4. Is this a variation of the Prisoners’ Dilemma?

1. Chris says:

This is actually another famous game from the world of game theory known as the Ultimatum Game. It has its own variations including the Dictatorship Game.

5. slw says:

If the stranger has no idea why I am offering him coins suddenly, then he is more likely to accept 1 coin than 5 coins. If he knows I am given the coins to share then he is most likely to accept 5 or more.

6. Miel says:

This was an actual experiment, but I think then the emphasis was on the other party: what offer would you accept? Both parties involved knew the rules exactly.

7. woupiestek says:

It is true that, if I offer the stranger at least 1 coin he will benefit from accepting. But I can’t help but thinking that in real live situations you should be more generous: I’m hoping that if the stranger is offered 100 coins to share some day, he will offer 50 rather then 1.

8. Carmen says:

I can’t see any reason to offer him less than 10 coins. It’s the best offer, the most likely to be accepted and the most rewarding for both.
I doesn’t matter how many coins you keep, if he rejects you lose them all.
bye

1. Alex says:

No, you’re splitting 10 coins. So if you offer 5 coins then you each will get five coins.

2. eggplantinspace says:

I agree with you Carmen. I went the other way at first, but you are right. It is the most likely way you will get something out of the deal.

3. Anonymous says:

You are completly right…the only thing to do is offer 10, it doesn’t matter what the other person knows about the set up,you are just betting on if they will accept or not. If they don’t you both get nothing anyway so why not go for 10, there is nothing to loose. People are over thinking this and asking too many questions and including too many variables. You have nothing to begin with and only one chance to get £10. I’m really surprises how many people both guys and gals go for 5?!

9. ChrisB says:

Tom, this is called the Ultimatum game.
Would have been interesting to know how previous knowledge of the experiments results change the outcome – if you factor in the most likely response of the stranger your own (rational) choice would change…

10. > If they accept your offer then you both get to keep the number of coins being offered.

Is this really what you meant? If I offer ten coins, and the offer is accepted then both of us get to keep ten coins?

1. Skepdude says:

I doubt that this whole thing hinges on a play of words that way. If you think about it, you’re offering two numbers, what you are to keep and what he is to keep, so if it is interpreted that way, which number would be the one used at the end?

11. Raymond says:

They did something similar on Brainiac. They offered people something for free, a free kettle I think, worth £10 and people took it without a second thought. When they offered people a £10 note people refused to take it. The assumption was when it was cash people thought there must be a catch where as free giveaways are more common.

12. Carmen says:

13. Personally it wouldn’t make a difference to me whether the other person knew all the rules to the deal. I would always offer half since it is money for nothing and that is the fairest outcome for everyone concerned.

I wonder if the amount of money involved would change the responces. Say it was 1,000,000 on offer. Maybe I might be more inclined to think that the other person would accept less than 50% as a good deal since it is still an incredible amount of money.

14. june says:

I also see no benefit to offering less than 10 coins.

Now, if I got to keep what I didn’t offer the stranger no matter what, that’s another story. Then I might keep the cost of something small, like a cup of tea or a used book. Or less, if the stranger successfully appealed to my sense of charity.

1. poccio says:

offering to keep means that you keep the amount

15. Andrew MW says:

There’re so many unknowns here I don’t really know where to start. “offering to keep” (in the poll question) is very odd wording. Did you mean just “offer”? And why isn’t zero an option?

1. Engywuck says:

Yes, I’m not a native. What does “offering to keep” mean??

16. If there are no further repercussions, then surely offering 1 coin is what you’d do?

If you offer nothing then there’s no incentive at all for the stranger to accept the offer.

If the stranger is a rational agent, then they’ll take anything above zero, given, as I said before, there is no further information and no further consequences.

1. ChrisB says:

Ah, but is the “rational agent” part a reasonable assumption? 😉

2. No, if you offered me, say, 3 out of 10, and I knew you got nothing if I rejected, I would reject out of spite.

/Z

3. Alex says:

Right, rejecting out of spite is a fairly common response to an offer that is too low when these kinds of experiments are run in real life. I don’t remember the exact stats, but there is a very high probability of deal rejection if you only offer one coin.

I do wonder how a much larger amount of money would effect the outcome. If I was offered 100,000 pounds out of a million, I think I’d still settle for the 100,000. For 1 out of 10, I’d definitely tell the offerer to shove it.

4. Indeed. That’s an important point too.

Is a dignified response worth losing 1?
Is it worth losing 100,000?

17. Bletherskite says:

It says that you can make one offer in which you might offer to keep 4 and give the stranger 6 so I assume from that they know how many coins you have in total.

I would say that offering a 50/50 split is the most likely to have agreement from the stranger whilst keeping a reasonable benefit for yourself. The offer of an even split would sound fair but if the stranger was offered a lower amount, then even although it was free money their sense of unfairness may kick in and cause them to reject the offer. Anything more to the stranger and you are losing out (although you may feel warm and charitable) and also you risk raising their natural suspicion as to why someone would give them something for nothing again causing them to reject the offer.

18. I would think that it would be that I could tell the person I had been given the money and told to share with another…..so to give less would be greedy and to give more than half might make the other person suspicious and refuse the money thereby both of us would have nothing…..so offer half to be fair and more likely to succeed in both of us have a nice day…… :}

19. I’d offer 2 coins.

And you better be thankful, prick!

1. FrankN.Stein says:

I – don’t think you will be lucky with that attitude … 😉

2. I’m not thankful, so there! And I refuse to play, so you get nothing. Serves you right for calling me a prick!

20. In the ultimatum game there is a difference, but only a psychological one: You’re BOTH given the money. One player decides how to divide it, and the other can accept or reject.

The second player will feel more entitled to a fair share if they’re both given the money.

Otherwise there would be no reason to reject free money. I’d accept 1 coin. Why not? To punish the guy? Fuck that. I like shiny coins. Mamma mía!

But if we’re both given the money things change.

21. mervulon says:

The wording here is tricky. ‘How many would you offer to keep for yourself?’ is a strange way of positing the question. And I think one must assume that the stranger understands the rules entirely, in which case a 50/50 split would be so clearly equitable that the stranger would accept the offer, without feeling slighted and consequently refusing out of spite.

22. Nikki says:

Superfreakonomics offers very interesting coverage of outcomes of different versions of the Ultimatum Game (including the Dictator Game). Highly recommended.

23. Gary says:

What is relevant here is the utility value of the offer balanced against the fairness of the offer to the stranger. Pretty much everyone would feel a sense of injustice at being offered less than an equal share of ten pounds and I would feel no meaningful loss at seeing both of us have nothing rather than an unfairness prevail. However, if the pot were 10 million coins and the split offer were still 9 to 1 the utility value of a million coins verses nothing with no negotiation, would force me to swallow my pride and accept. Million coins is a million coins after all.

24. Mark H says:

“Offer to KEEP”, people, “offer to KEEP”.

Anyone who offers to keep less than 5 just hasn’t understood the question.

[“Offer to keep” is a very ugly wording incidentally. How many would you “offer” would be less ambiguous for sure.]

1. Chris says:

Either that or their incentives are different to purely monetary gain.

2. FrankN.Stein says:

wrong – anyne who offers to keep less than 5 can asume to please the stranger by offering him a bigger share, thus teasing him not to give in to his greed and ask for even more than that. (Or if you offer to keep only one, you can be 100% sure that he accepts it and you have at least the one.)

3. Engywuck says:

Now I may have understood the question. Maybe this wording did confuse many others too!?

25. Chris says:

We did our own experiment with this set-up for which I had to write a computer program. Like you, I also forgot players may choose to take 0 which, unlike you, forced me to do some rather creative last-minute editing!

26. I don’t see why a stranger would reject any amount of free money offered, even if they knew that you got more.

27. Assuming both players in this game theory game are perfectly rational (which is a huge assumption, admittedly), it would be in your best interest to offer to keep 9 coins, therefore giving the other player 1. It still betters his position, so if he’s perfectly rational, he’ll accept, and it maximizes your payout (which is always good. 🙂 )

1. mervulon says:

And what, then. do you do when the other player says, “Give ME nine or get nothing”? Which would be an understandable position to take in response to the inequity of your original offer…

2. Right, mervulon. That’s very relevant. The game becomes a bargain and the roles (offering and accepting/rejecting) are lost.

Something should be done against that possibility for the game to work.

3. Actually… I take that partially back.

The offered guy can be bluffing.

The offer will still be made by the first
guy, and the second one can accept in
spite of having said that he wouldn’t.

4. Chris says:

Which would turn this into game involving signaling. I ❤ Game Theory.

5. Haha, indeed. But that
could be avoided too,
by avoiding contact
between the two guys
(except for an envelop
with the offer).

I♥GT2

6. seePyou says:

The rules are stated already. Quoting “You are allowed to make just one offer” which to me says that the other party can just say Yes or No, no bargaining.
This just proves that people overcomplicate a simple game (as the title suggests) to try to find the “better” deal for themselves without considering the simplest truth: best course of action is what is good for you AND the whole, in which case offering half, like most people offered. You dont have to offer less than five or more, 5 each is perfectly reasonable and fair and profitable. Greed (offering more) or fear of rejection (offering less) are extremes that are both less than optimum.

7. Of course. Just one offer.
Nevertheless a little chat
could happen before that.

I’d offer a 20% of a big
amount if the other guy
has to make a quick
decision after learning
the rules of the game.

It IS complicated, seePyou.

Fairness is overrated and subjective.
Free money is objective.

28. Gus Snarp says:

I’m confused, what are these coins that weigh ten pounds and how many of them are there?

29. FrankN.Stein says:

Fair is fair… I would not and would not want to give him less than 5, considering we are both into this. And i he gets greedy and mean, blowing it by asking for more than 5 – I rather live with losing the whole deal than reward greed and unfairness.

30. Nah. “Fair is fair” my ass.
“We’re both into this”, but
we’re not playing the same
role.

It’s important to distinguish
the situation where the two
exchange before the decision.

People have an instinct to
teach people lessons. But for
them to qualify as people we
have to know them, see them…

31. Skepdude says:

I guess the assumption is that the stranger know all the facts as we do. So why would he agree to anything less than 5, and why would I? 5 seems to be the only answer that would be acceptable by both parties.

If he does not know of the condition on the other hand, you offer him 1. Immagine if someone walked up to you and said “Hey, I have these 10 coins and I’m gonna give you one and keep only 9 for myself”. You’d take the 1 coin.

32. It helps to suppose that ten pounds is a reference to the weight – I would not wish to carry around 4.5359237 kilograms in coins so I would give most of them away.

33. Magnus says:

Where is the option for keeping zero?

34. glen says:

Digressing just a bit into the interface, why is 10 an option to click on when the rules say “You have to share the coins with a stranger.”.

Shouldn’t the biggest value be 9?

(Sorry, my inner programmer is coming through)

35. jk says:

well it depends if its someone i like or not.
If its like my best friend id give them 6 pounds/euros,
but if its someone i hate, (Jimmy Carr) id give them 1pound/euro

36. Keep 10 and they get 0.

If someone said “Hey, I’ll give you 0 coins” I’d prob just laugh it off. no need to reject getting 0 coins.

37. Stephen says:

It’s not so difficult. Everyone profits if the choice is made to accept the money, even if the money is only £1. People may as well choose to keep £9 and give £1 away, as a free pound is better than no money. Jealousy and the desire to thwart greed kick in to spoil that plan on the part of the chooser, though.

38. Astrosonic says:

I just did an experiment on this in Glasgow uni and there was deception involved. The offerer was given the instructions to keep £9 and thus I was offered (I wasn’t aware of the deception, obviously) £1. I was told of the rules in the beginning. The experimenter wanted to prove some statement wrong, which asserted that people will accept any kind of offer. Apparently most people still accepted the £1, as did I ’cause it was the rational conclusion, wanted some compensation for my time. But hell I was furious, threatened to punch the other guy if I see him again =) and slightly regretted my choice. In the end I was debriefed and got £5. No need to punch anyone =P

39. SteveG says:

If the other person knows the rules I still think they may accept whatever you offer. The only thing they can do is play the spoiler so we both get nothing. To do that he would have to be insulted (or stupid) and blow the whole thing. Since he’s a stranger and I don’t know how he’ll react, I’d offer him 4. Not as much as me but enough to keep him interested.

Since I’m starting with 10 and he’s just standing there being strange, I don’t perceive us as having equal investment in the game, so I think I should get a little more.

I don’t know what that says about me…

40. Mchl says:

Why can’t I offer to keep 0 coins?

41. Rosie says:

When I voted, I assumed that “you both get nothing” meant that you’d lose even the coins you tried to keep if the stranger rejects your offer. From the comments it sounds like you only risk the coins you offer. I wish I could revote now.

It sounds like a variation on ads that say, “buy our product because the proceeds go to X charity and you’ll be entered in a raffle”.

42. Paul Delaney says:

This psychologic experiment was summarized quite nicely in “SuperFreakononics”…. the main point of the authors being that as a psychological experiment it lead to conclusions that were not supported in real-world testing.

43. theboywil says:

I figure that you don’t have to disclose the amount of coins you started with (and that you can’t tell the stranger that if they accept then you both get to keep the coins..)

Then figure that if you offer someone a single coin they are more likely to accept than offering any multiples of coin.

44. Berber Anna says:

It doesn’t matter whether the other player knows the rules, or what’s most profitable to me. I offer five, because I’ll feel guilty if I don’t. I’m no better or worse than the other player, so we should share equally.

45. I’m the younger of two sisters. My sister and I would practically get out a ruler when dividing a candy bar to ensure we each got an equal portion. Ergo, I’d most likely offer a 5/5 split.

Too many unknown variables.

IF:
– Hey, I got £10 from that guy, and he said I should split them with you.

THEN: I would probably offer the stranger £5, which is the inconspicuous standard split.

My vote: Male, 5 coins.

If we really get the same amount anyway, it would be better to offer all ten coins, but the stranger might get more suspicious about that.

Unless I’m wearing fancy clothes and appear obviously rich. Then I could say that I got £10 from somewhere, and say: “You want them?”

48. rebecca burgess says:

same as most ppl, try to spilt it both ways, and if they refuse, then, meh! Its only £5!

49. I’d keep £1.

If you take £5, yeah, you’ve made a fiver, and they have, and you’l both go home feeling exactly the same and not really being any richer in the grand scheme of things.

If you take more than £5, the other person might accept it, but if they understand the rules of the game they’re going to feel a bit pissed off/ resigned.

If you only take £1, you won’t be missing much, and the other person will get, as well as the money, a puzzle as to why you did it. Any maybe they’ll think a total stranger was trying to do something nice for them, which is likely to provide more happiness than any sum under £10 could for most people, especially if it gets them thinking about people differently.

Or to look at that another way, you get to be all idealist and happy (see above!!!) imagining you’ve made someone’s day, even if in fact the recipient’s only thought is, “Ha! One born every minute eh?!” So take a pound to make yourself feel better 😀

50. Eddy says:

I received an email version of this recently. A Nigerian gentleman (actually a former prince, would you believe) had come into a sum of money, and was offering to split it with me — a complete stranger. If I didn’t accept his offer, he would be left unable to extract the funds, so we’d both lose out.

He was only offering me a meagre 20% of his \$7,500,000 horde though, so I told him to stuff it.

51. Looks like a variant on the prisoner’s dilemma from Game Theory.

52. Hey, you have a great blog here! I’m definitely going to bookmark you! Thank you for your info.And this is Game Varaity Social site/blog. It pretty much covers Game Varaity Social related stuff.

53. graeme says:

This is a game theory classic – shamelessly lifted from Wikipedia – http://en.wikipedia.org/wiki/Pirate_game

There are five rational pirates, A, B, C, D and E. They find 100 gold coins. They must decide how to distribute them.

The pirates have a strict order of seniority: A is superior to B, who is superior to C, who is superior to D, who is superior to E.

The pirate world’s rules of distribution are thus: that the most senior pirate should propose a distribution of coins. The pirates, including the proposer, then vote on whether to accept this distribution. If the proposed allocation is approved by a majority or a tie vote, it happens. If not, the proposer is thrown overboard from the pirate ship and dies, and the next most senior pirate makes a new proposal to begin the system again.

Pirates base their decisions on three factors. First of all, each pirate wants to survive. Secondly, each pirate wants to maximize the number of gold coins he receives. Thirdly, each pirate would prefer to throw another overboard, if all other results would otherwise be equal.

===

Your task is to figure out the best way to distribute spoils such that all the pirates buy into the deal and nobody gets thrown overboard.

If you keep adding pirates to the pool then surprisings things happen when the number of pirates reaches 100 and again when it hits 200, after that it just gets weird.

The solution for 100 pirates explains why you should only keep £1 in this situation.

54. blue says:

I would very much like to answer the poll, but like the others, I am confused as to what the question is asking and exactly what the details/rules are. Does the other person know what you’re doing? Are you both getting the amount of coins you are offering to keep for yourself, and it’s just a trick question? Does the other person know there are 10 coins, or how many you will keep vs. how many they will get, or that you’re giving to get? Do non-monetary “gets” really count (I don’t see how they could, since I’d be bound to get something out of the interaction, whether amusement, frustration, annoyance or whatever).

My initial reaction (I’m female, btw), assuming they knew the amount of coins, that they were aware they were the ones in control of whether or not we got anything, and a few other baseline assumptions, was to keep 5 coins for myself and offer them 5. That way seems most likely to get them to accept, since no one could say it was unfair, and we’d both gain. Of course if we both keep the amount I offer, I’d offer 10!

55. Interesting curiosity, but what does this experiment teach?

It only shows that the receiving person is not a robot only looking at the gift (a gift of one coin is better than nothing), but a human which may get a sense of unsatisfaction at your offer. That unsatisfaction is subjective.

This is nothing new or surprising.
What is more important here is what the experiment teaches us about the experimenter. In this case, and although it was mot explicitly called out, I suspect that the experimenter has some wrong incorrect of “rationality”. I am curious to read the experimenter’s interpretation of the results…

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