You are in a game show with nineteen other players. You don’t know the other players, you can’t see them, and you can’t communicate with them. The game you are in is called ‘Greed!’, and is straightforward to explain. You are asked to write down a whole dollar amount in the range $1 - $1,000,000 on a piece of paper. You will be paid the amount you asked for if it is deemed to be ‘non-greedy’. Whether your request is indeed ‘non-greedy’ will be decided once all twenty request have been received by the host of the show. Your requested amount will be labeled ‘non-greedy’ if no other player has asked for less, and at least one player has asked for more. How do you play?

…is good

Say $1, take your dollar to the strip club, and Eff everyone else!

It would be in everyone’s best interest to all write down 1,000,000

>It would be in everyone’s best interest to all write down 1,000,000 Why? Then it would be considered greedy…

^True but with no punishing mechanism there is no disincentive to defect to say 999,999.99.

I would go with $1. Just to F the thing up…and proceed to said strip club.

Isn’t this much like prisoner’s dilemma?

No, because you have nothing to gain by being an “@$$ hole” here.

If you write down $1, you have to assume that the other people are rational as well. In this case, everyone else will put $1, and everyone goes home with nothing. It is similar to the 2/3 average game: http://en.wikipedia.org/wiki/Guess_2/3_of_the_average Guess 2/3 of the average is a game where several people guess what 2/3 of the average of their guesses will be, and where the numbers are restricted to the real numbers between 0 and 100. The winner is the one closest to the 2/3 average.

Well it all depends on whether there’s a female player with a solid 34-C.

As much as I hate to agree with Sanka’s Mom, it does seem that if you assume that all participants are rational and have knowledge of each others’ rationality, the answer will converge to $0 or $1 - both of which are equivalent. This is how it works: 1) No one will say $1,000,000, since that precludes the possibility that someone else will be higher than you. This means the max payoff is now $999,999. 2) You will not choose $999,999, since you know no one will choose $1,000,000. So the max payoff is now $999,998. 3) However, you will not choose $999,998, since no one will choose $999,999. 4) Repeat this sequence until you reach a maximum payoff of $1. If you choose $1, you will get zero payoff since no one will choose $2. This is equivalent to choosing $0. On a side note, the optimal collusive strategy is for one person to choose $1,000,000 and for the rest to choose $999,999.

Hello Mister Walrus Wrote: ------------------------------------------------------- > As much as I hate to agree with Sanka’s Mom, it > does seem that if you assume that all participants > are rational and have knowledge of each others’ > rationality, the answer will converge to $0 or $1 > - both of which are equivalent. > > This is how it works: > > 1) No one will say $1,000,000, since that > precludes the possibility that someone else will > be higher than you. This means the max payoff is > now $999,999. > 2) You will not choose $999,999, since you know no > one will choose $1,000,000. So the max payoff is > now $999,998. > 3) However, you will not choose $999,998, since no > one will choose $999,999. > 4) Repeat this sequence until you reach a maximum > payoff of $1. If you choose $1, you will get zero > payoff since no one will choose $2. This is > equivalent to choosing $0. > > On a side note, the optimal collusive strategy is > for one person to choose $1,000,000 and for the > rest to choose $999,999. you cannot assume rationality when the expected value of all participants being rational is $0. thus, i believe the most rational thing to do without the assumption that all with act rationally is to ask for $49,999 as most participants will be looking to maximize their share of the $1,000,000 and would likely post $50,000 or greater. you may wish to put $49,998 as someone may have the same line of thinking as you.

Assuming the other contestants are average people off the street, rationality is out the window. It is safe to assume some idiot won’t understand the rules and will ask for the full $1,000,000, so having at least one player asking for more is covered for everyone except the idiot. Then I think you have to decide what you think the average person on the street would consider to be a decent amount to walk away with. Although few people would turn down a couple grand, I think your average Joe is going to want to walk away with at least $10,000. Chop $2,003 off of that as a safety margin and go in at $7,997. Of course if there really are a couple of rational AF’ers in the contestant pool, someone will say $1 anyway, and you’ll walk away with nothing but that was going to happen anyway.

Simple backward induction and the answer is $1 with no bargaining. A better game is to study the value of revenge that participants get. Similar set up except 2 players, fixed pot of $100. One player writes down a specific amount 0

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very good point by mattlikesanalysis. “rational” in this context does not mean follow some algorithm blindly regardless of what the outcome is. if your “rational” actions result in a guaranteed zero payoff, why the hell is it rational to follow them? only an irrational person will follow the “rational” algorithm of choosing zero

You cant break the rules of rationality because you dont like the outcome. While I agree that the payoff isnt desirable, you cant change the rules of game theory and redefine rational to meet this particular game. Until we have a better model for defining limited cognition and behavioral theory, which is the focus of many economists, you need to go with the models that you currently have.

^^^Somebody studied game theory. We actually used to do that exact game for real in school, plenty of willing, poor undergrad participants and so much easier than a smoking study, haha.

^^Yeah my ex Prof was doing this study on the intangible value of revenge when I was in grad school and I helped him out a few times. I think he was actually published for his work in Econometrica.