You are in a room full of 100 perfectly rational people. They are all motivated to personally make the most possible money. The rules of the game are as follows.

1. Without any communication with each other, each person writes "contributor" or "parasite" on a slip of paper with his name on it and submits it to the game's moderator.

2. The moderator goes through the slips and records each player's choice. For every contributor he takes $100 from the moderator's treasury and puts it into the Game Bank. For every parasite he removes $200 from the Game Bank, possibly making it go negative.

3. He gives each contributor 1 share and each parasite 2 shares.

4. Finally, he distributes the Game Bank to the players according to how many shares they have. If the Bank is positive the parasites get twice as much as the contributors. If the Bank is negative the parasites owe twice as much as the contributors and they all must pay up.

What is the perfectly rational strategy for the players?

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The game theory solution is for each player to randomize his choice, picking parasite with about 1/3 probability and contributor with 2/3 probability. A room full of game theorists break even in the game.

My contention is that the perfectly rational choice is to be a contributor. A room full of perfectly rational people each make $100.

PairTheBoard

what about a room of perfectly rational people thinking on different levels from one another?
or

if they all think on the same level, then it should reason that they all make the same choice.
-> i.e. i know my competitors think that if everyone selects contributor then we will all benefit some. however, if i select parasite with all of them selecting contributor, then i will make more money. still, if they also have the same thought process as i, then we could all end up selecting parasite and going broke.

i think selecting contributor is the most appropriate chioce. a penny saved is a penny earned.. no?


also, this reminds me of the prisoner's dilemna:

"Two suspects are arrested by the police. The police have insufficient evidence for a conviction, and, having separated both prisoners, visit each of them to offer the same deal. If one testifies ("defects") for the prosecution against the other and the other remains silent, the betrayer goes free and the silent accomplice receives the full 10-year sentence. If both remain silent, both prisoners are sentenced to only six months in jail for a minor charge. If each betrays the other, each receives a five-year sentence. Each prisoner must choose to betray the other or to remain silent. Each one is assured that the other would not know about the betrayal before the end of the investigation. How should the prisoners act?"
- wikipedia

By all stating that all the players are perfectly rational then all the players must take the same decision. Given that all players will make the same decision as me, the best strategy for me would be to contribute.

By wording the question as you have you have in effect allowed a player to choose his strategy and those of the other players. However when players make their decisions independent of the other players, then as any one player can improve his pay-off by changing his strategy, then "always contribute" cannot be the optimum solution.

Your argument that contributing is the rational solution, is backwards. It assumes that since all rational players will play the same strategy the rational solution is to maximise the total pay-off for all players. But the strategy is only the same for all players because the question supposes that all players are rational, and so this fact cannot be used to determine what the rational solution actually is.

EDIT: Though the rational solution is the one that fairs best against itself, this is not the same thing.

They are all motivated to personally make the most possible money. By "perfectly rational" I mean they each seek to find the optimum strategy to achieve that goal. They are selfish and smart enough to understand things like game theory. Nobody is playing to personally lose and nobody is unable to think things through. Nobody is just guessing.

A player need not just pick "contributor" or "parasite". He can randomize his choice by fipping coins or spinning a wheel if he wants.

It's not necessary that each player thinks identically. Only that their thought processes work perfectly well.

PairTheBoard

EDIT: The best strategy must be the one that fares best against itself. Since playing parasite fares better against "always contribute" than "always contribute", the later cannot be the rational solution. But then you know this, you put in the OP.

Why do you think always contributing is the best strategy?

Contributing 100% is only rationale if you know everyone else is going to do what you do. But then again if you know what everyone is going to do it would not be a game now would it.

Again this is greed/most optimal vs. certainty and low risk of having to pay. Also personal gain vs. shared gain and where u put ur priorities.

At first i'd go with the calculated randomization on this one. You just have to be lucky enough to draw to parasite, but since everyone has a fair shot at this, you can't really complain when you draw to contributor.

So yes, build the pot with as much parasites untill it continues to be no longer profitable. But in your example with the 2/3 1/3 distribution, no one will make a penny.
If 67 contribute and 33 parasite, there is only 100$ left in the Gamebank. Parasites are taking 200$ of the Game pot, but their 2 shares wont garantuee 200$, not even over 100$.

Selfishness and an optimal choice for yourself are properties of most Gametheoretic problems. Here selfishness and an optimal choice for yourself does not serve all, and therefor yourself, being a part of all.

Gamebank after 0 parasites: $100000
Nr of shares: 1000
Worth of share: $100
0 Parasites get $200 and 1000 contributors get $100

Gamebank after 142 parasites: $57400
Nr of shares: 1142
Worth of share: $50.26
142 Parasites get $100.52 and 858 contributors get $50.26

Gamebank after 333 parasites: $100
Nr of shares: 1333
Worth of share: $0.07
333 Parasites get $0.15 and 667 contributors get $0.07

So selfish behaviour will reward the parasites up until 14 parasites in a room of a 100.
They will earn more than $100. Up until 33 parasites in a room of a 100 will make the gamebank go negative.

So if the players value selfishness over certain gain for all of them, they should let the dice decide which ones of the 14 will be the lucky ones that stand to gain more than $100, while profiting of the contributors who will only receive about 50 bucks. If the players value certain gain for all then nobody should be a parasite, making the Gamebank the largest, and the shares worth the most. If players can not trust eachother and go for selfishness and optimal gain above all, then a controlled random distribution of 1/3 2/3s seems about right.

Edit: the rational people in the room should eventually stop playing against eachother, and realize that the true opponent they are collectively playing is the GameModerator. Therefor to pull the most money out of the GameModerator pocket into their pockets, they should favor a theory that makes the GameBank the biggest, hence all pick contributor. They should act as 1 opponent.

The "if .... then" logic you present is the one used by game theorists. That logic is available to all the players and thinking it through arrives at the game theory solution I gave in the OP. Randomize your pick with about 1/3 probability for parasite and 2/3 probability for contributor. If everyone succeeds in thinking this through to this conclusion then there will be about 1/3 who choose parasite by chance and 2/3 who choose contributor by chance. You might think this is therefore the rational strategy. Unforunately, a roomfull of such rational people will only break even.

My contention is that they have stopped thinking too soon. If we must accept that the logic of game theory dictates what is rational then I contend there is a superrational choice of choosing to be a contributor. You can arrive at the superrational choice by realizing it is the one which will do better than break even for everybody. The superrational choice makes everybody $100. That makes it clearly superior if everyone realizes it. But there's no reason why they shouldn't. If you can so can they.

Here's the really "super" part of the idea and the catch. You can only fully realize that it's the superior superrational choice by making it. You essentially discover the logic in it when you make the Contributor choice. Those who reason like you suggest above do not fully realize that it is the superrational choice. You must actually make the choice to fully discover and realize its superiority. So your guy cannot depend on the notion that anybody else is making that choice. Your guy is left falling short of complete follow through in his thinking and can only continue down the game theory line to a conclusion of randomizing his option.

But if I am thinking perfectly well and I realize the superrational decision by actually making the Contributor choice, there's no reason why everybody who thinks equally well won't do the same. We all fully realize the superrational by actually choosing Contributor and are each personally rewarded with $100 more than the short sighted game theorists in the room next door. They did not have the ability to think things through all the way.

Also, I think this idea has broad implications. As far as I know it's new and radical. But so was Nash in his time.

PairTheBoard

Why not go one stage further? If everyone is playing the "superrational " strategy of "always play contribute", I'll play the "ultimate-rational" solution of "always play parasite", why must the players stop at the "superrational" when an individual can make a clear improvement. Neither strategy is stable as it isn't optimal against itself.

This thinking is levels is precisely why the Nash Equilibrium is to play the mixed strategy you noted the OP. It's not the game theorists who have stopped thinking too soon, but the "superrationalists".

That said, your argument isn't without merit, it's why the strategy "always defect" isn't optimal in the infinitely repeated prisoner's dilemma, but in one off games, a strategy cannot be optimal if the best strategy against it is something other than that strategy.

In the one-off game you propose, how the roomful of players does is irrelevant to the individual player, so you can't use that to demonstrate one strategy is superior to another.

I think this isn't correct. You profit by choosing parasite up until 32 other parasites in the room, because you always make more money as a parasite than as a contributor.
Yes, the parasites as a group of 15 to 33 would be better off ALL choosing contributor than ALL staying parasites. But I would say this is irrelevant under the game conditions.

The wording was off. Up untill 14 parasites would stand to gain more than $100 was what I was trying to say. Because $100 is the default for everyone if all go contributors, this seems like a threshold.

If the parasites make less than $100 and the contributors far less, the game moderator is laughing, and has viewed the selfishness destroy overall value. Your goal should not be to make more money than 'opponents' in this room, your goal should be to make most money of the game moderator. The first goal conflicts the second.

You need the trust of working as a cohesive group to make a fist against the game moderator. Else you could just as well cheat on the randomtest, and fill in parasite when commanded by fate to fill in contributor.

More than 14 parasites in a group of 100, will make all lose money against the main opponent (the one who is giving out $100 to everyone garantueed), which is the game moderator. Employing selfish goals when being part of a group that suffers from these very choices is not rational nor optimal.

Making more money as a parasite than as a contributor should not be a goal in this game. Making the most money combined is the goal imo.

Neither nor. Your goal should be to make the decision that leaves you with more money than the other choice.

Why?
Well, maybe if you know the moderator is super-rich and/or does bad things with his money, then yeah, there is additional value in taking the most possible money off him as a group.

But I think this might show that the problem has insufficient information or a wrong premise. Isn't it reasonable to expect from "perfectly rational people" to consider more factors than just "personally making the most money"?

You've just repeated the same objection I already responded to. Your step forward to the ultrarational is not a step forward from the superrational but a failure to step forward from game theorist logic to the superrational. You didn't address the points I made at all. You can't step forward in thinking from the superrational because you only fully realize the superrational by actually making the contributor choice. Once you do that you're done.



PairTheBoard

EDIT: What FoldALot said.

Why isn't it a step forward? If I anticipate everyone being superrational, then playing parasite gives me, the individual, a bigger pay-off from playing the superrational - which seems like a step forward to me.

The superrational solution is only superior as long as we assume all the players must make the same decision that I do, which I've already conceded is the case.

Well you still need the trust. If you expect the chance of only someone cheating on the randomtest and forcing parasite to be great, that should influence your own choice to stay true to the randomtest and maybe force a switch to contributor to cut your losses.

Edit: Let's say you decide to play the scenario twice. First time you are freerolling so the aim should be to funnel as much money into the system as possible. Which means everyone picks contributor and game moderator leaves poor. Now you play the scenario again, but the money is in the pot is already yours. If you pick parasite you get 2 shares but we burn $200 from the gamebank. Contributors gets 1 share of the gamebank. Will you still pick parasite as to potentially earn more than someone who picks contributor?

Why is that?

I think it wouldn't be hard to make up a scenario like the one in the OP, where people are all perfectly rational and still decide differently, because "people" come from different backgrounds and have different goals in life.

Or not?

Can anyone give a definition of "rational"?

Of course. In the real world it we all make decisions based on our preferences, it is rational for me to buy vanilla ice cream when faced with the chance to buy chocolate or vanilla, but for others it's the other way round.

When dealing with artificial games like the one in OP, rational is usually taken to mean that the individual is concerned with maximising his pay-off for the game, which in this case is to maximise the amount of money he can make from it, and acts optimally to achieve this.

Because the players have identical aims, then they will adopt identical strategies, this is a feature of the optimal strategy solution. But it doesn't follow from this that one player can realise that all players must think identically to him and if he changes his strategy all others also will.

I'm a bit confused now.

Adopting identical strategies doesn't necessarily mean they all end up with the same decision, right? For example if they choose a game-theoretic approach and randomize their decision. [Does the OP say 'game theory = not rational'?]

Sorry, by choose the same strategy I meant something like "play contribute 2/3 of the time, and parasite 1/3 of the time" not that they all would make the same decision between parasite and contributor. If they all choose the same strategy but it's mixed (i.e. sometimes do X and sometimes Y) then yes they don't necessarily have to choose the same thing.

I think this is where you are making a mistake.

"The superrational choice makes everybody $100." No. It costs the Bank $10,000.
It IS a zero-sum game if you include the Bank, so the 101 participants will break even no matter what. And nowhere did you say the game is about rational people vs. Bank. You explicitly said "personally". So why would you care more about the other people than the Bank when making your decision?

Originally Posted by PairTheBoard
You can arrive at the superrational choice by realizing it is the one which will do better than break even for everybody. The superrational choice makes everybody $100. That makes it clearly superior if everyone realizes it. But there's no reason why they shouldn't. If you can so can they.



You don't. But you recognize that if everybody makes $100 then you make $100 instead of the Zero when the game theoretic strategy is determined best. That's what you care about. You recognize that you personally making $100 is better than you personally making Zero and you recognize that everyone else should be able to see the same thing. That the superrational strategy is best.

But so far, everyone has ignored the real core of my argument whereby I claim that the superrational strategy can only be fully realized by a participant when he actually goes through with chosing contributor. The strategy cannot be fully realized as the superrational best one which everyone will employ by just thinking about it. It must be acted on for a player to fully realize its superrationality and the clearly superior one which everyone will settle on. This is the novel idea. If you don't get this you aren't really on the same page as me and our replies to each other are just repetitive.

You might read the concurrent thread about a Problem of Expected Value. My idea here is similair to the one first presented there by Madnak about causative source variables determining both the choice and the prediction of the choice. In that thread I observed that you can't know the sum of the causative source variables until you actually make your choice. Your choice doesn't determine the sum of variables. You discover the sum of variables in the action of actually chosing.


PairTheBoard

Well to be honest, I don't get it (not your fault). But I would love to, because it's certainly interesting.

Let's dumb it down for me:

Case 1
You actually go through with your superrational choice of Contributor. Later you receive $100 from the Bank, which means that everyone in the group has made the same choice. You now realise that if you had chosen to be a parasite, you would have received $192.08. So in this particular case, you did not make the most profitable choice.

Case 2
Again you go through with your superrational choice of Contributer. You receive $20 from the bank. You now realise that if you had chosen to be a parasite, you would have received $34.92.
But even more worrying is the fact that 25 individuals out of the group of perfectly rational people did NOT go through with the superrational choice, for whatever reason. "What the heck is going on?????", you ask yourself.

Okay, so let's stick to Case 1. If it turns out that way, you KNOW for sure you would have done better by choosing parasite. Of course that's results-oriented thinking.
But since you are aware of the possibility that it can turn out you would have done better with the other option while you are going through your choice-making process, how can you ever realize the superrationality of your choice during that process?

So you're saying you assume everyone else will be a contributor. If that's the case then there is nothing rational about being a contributor yourself. Personally making $100 is worse than personally making $194.

Which means that it CANNOT be the optimal one; there must be a supersuperrational strategy.

I don't think your superrational theory is novel. It's very similar to David Gauthier's analysis of Kavka's toxic puzzle, which is based on the same principles as the paradox in the other thread.

Those paradoxes are completely different to this game though because in those paradoxes you are not playing against other players concerned with their own pay-offs, but instead with an omniscient actor whose strategy is solely dependant on what he believes your action will be. Because your "opponent" in the paradox is omniscient when you choose your strategy you effectively choose the strategy of your opponent. This causes a paradox because it is an example of reverse causality.

As I have stated, in this game, if we assume our strategy change would identically change the strategy of all players, then contribute would be the best strategy.

However, your opponents strategies are not based solely on the perfect knowledge of your strategy; this means that if we alter our strategy then it doesn't follow that our opponents will alter theirs. Because of this we cannot assume that a deviation from the game theory optimal strategy will be followed by all. So if an individual player has an incentive to play strategy x when all others are playing strategy y, then strategy y cannot be the best solution.