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Unread 06-07-2009, 06:36 PM
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Funding Dilema (game)

This is hypothetical and thus why it is in Chit-Chat. Think of it as a bit of a game.


So you approach a potential sponsor looking for some cash for you team, and the sponsor tells you, "Funny, another FIRST team asked me the same thing." He then tells you he has an idea. "I will pose the same idea to you and the other team. Based off of your answers, I will support one or both of your teams. You both will be given the choise to Share, or not share. If you choose to share, I will give each team $400. If you choose to share, but the others do not, I will give $1000 to the not sharing team and $0 to you. If the other team chooses to share, but you do not, then I will give you the $1000, and the other team nothing. If you both choose not to share, then you both will get $1."

What would you choose? If you feel so inclined you may also answer why.

Suppose that you only found out the answer after pay off, but you knew that you would be getting this same response from multiple donors (and you an the other team are the only ones talking to the sponsors). Would this cause you to change your answer, an if so how?
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Unread 06-07-2009, 07:24 PM
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Re: Funding Dilema (game)

As a fervent optimist and a believer that all things happen for a very good reason I would have to say that I would offer to share the money.

Rational: $1000 is significant, but I think that we could live with $400. Besides, sharing the money would be so much more gracious and we could go on with the satisfaction that we were willing to tighten our belts for the benefit of a fellow team. If the other team doesn't feel the same way and chooses that they don't want to share the money then at least I can convince myself that they obviously had a greater need of the money then we did. Might be a bit of a naive viewpoint, but I for the moment have a very high opinion of the FRC teams that I've encountered.

By the way I love the puzzle. I love philosophical/moral challenges. Please post any others you think of.
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Unread 06-07-2009, 07:58 PM
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Re: Funding Dilema (game)

Great reimaging of the classic death penalty/5 year suspended sentence riddle.

Share. I can't imagine a team in the Indianapolis area (or anywhere else for that matter) I'd want to shaft. If they do it to us, then I suppose that would show where their priorities lie, eh?
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Unread 06-07-2009, 08:29 PM
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Re: Funding Dilema (game)

If it's another FIRST team, share.

Why? Because if they choose not to, you get nothing. You can always raise money. If they choose to share, you get $400. But if you choose not to share, and they choose not to share, you'd be better off asking team members for their loose change.

Not to mention the whole reputation thing, and that because this is a FIRST team we're talking about, it's more likely that both of you get the $400.
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Unread 06-07-2009, 10:04 PM
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Re: Funding Dilema (game)

I would share. I feel that besides being gracious, the money isn't that much, you would need to hurt the other team ten time just to apply to two regionals. I would prefer to sleep at night than get 600 dollars that won't pay for one student to go on a trip.
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Unread 06-07-2009, 10:41 PM
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Re: Funding Dilema (game)

The Prisoner's Dilemma, but applied to FIRST.

In this case, I wouldn't take their money. They're financially rewarding sabotage, and encouraging acts that would make no one's grandmother proud. I wouldn't judge the other team for being desperate for cash, though. They might need more than $400 and be out of options, and it would be unfair of me to think of them as un-GP...

If you're going to deny a FIRST team money based on one of the teams being extremely GP, the sponsor clearly doesn't get FIRST, and I want none of their money.

If the sponsor secretly would give neither team money unless they both shared, now that would be different. A valuable lesson rather than manipulation.
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Unread 06-08-2009, 07:08 AM
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Re: Funding Dilema (game)

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Originally Posted by Chris is me View Post
The Prisoner's Dilemma, but applied to FIRST.

In this case, I wouldn't take their money. They're financially rewarding sabotage, and encouraging acts that would make no one's grandmother proud. I wouldn't judge the other team for being desperate for cash, though. They might need more than $400 and be out of options, and it would be unfair of me to think of them as un-GP...

If you're going to deny a FIRST team money based on one of the teams being extremely GP, the sponsor clearly doesn't get FIRST, and I want none of their money.

If the sponsor secretly would give neither team money unless they both shared, now that would be different. A valuable lesson rather than manipulation.
My thoughts are that FIRSTERs probably tend towards the Superrational group more so than to the Rational group. This may be the first response I have ever seen that is UberSuperrational. Probably a scarce breed because they would die off in a competitive world, but refreshing to see. (By the way, it could be argued that this sponsor is trying to teach a valuable lesson of the benefits and dangers of cooperation. If you work at a food bank, it would be silly to starve yourself to death.)

I probably should have set this up as a blind poll as that is an important part of the experiement. There are still a few interesting arguments I have not seen yet. The values were very specific (at least in relative scaling). For those of you that have recognized Prisoner's Dilema, congrats. For those of you that haven't heard of it, think about what you would do before reading up on Prisoner's Dilema. You don't have to post, but I do ask that you think before reading (I would be thrilled if you do read about it though).
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Unread 06-08-2009, 07:46 AM
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Re: Funding Dilema (game)

The first question when playing a game like this is to establish what your objective function should be. Normally in the prisoner's dilemma, the objective is to maximize your payoff without considering your opponent's. However, one could certainly make the argument that in the case of FIRST the objective should be to maximize the total amount of sponsorship for both teams without worrying about who gets what. Interestingly, examining the "worst case" payoff matrix for the game as posed yields what I believe to be the first mathematical proof of GP...

Here is the payoff matrix of IKE's game:

A shares, B doesn't - $1000 total
B shares, A doesn't - $1000 total
A shares, B shares - $800 total
A doesn't, B doesn't - $2 total

The first thing we need to mention is that the game has to be double-blind in order for there truly to be a dilemma. If one team can contact the other, then arranging a $1000 donation to one team that then gets shared 50/50 would be the optimal fair solution. But let's imagine we can't do this...

Clearly, one team sharing when the other does not yields the maximum total payoff. However, if you don't know what the other team is going to say, you can't be sure that you are arranging this scenario (i.e. you need to know what the other guy is going to say in order to say the opposite). So let's examine what happens if team A chooses either option...

If A won't share, the best possible outcome is that B decides to share ($1000 payoff). The worst possible outcome is that B doesn't share ($2 payoff). Assuming that B has a 50/50 chance of choosing either, the "expected value" (EV) of A's "don't share" decision is (1000+2)/2 = $501.

If A does share, the best possible outcome is that B does not ($1000 payoff). The worst possible outcome is that B shares as well ($800 payoff). With the same 50/50 assumption, the EV is now (1000+800)/2 = $900.

Clearly, in both the worst case ($2 vs. $800) and "average" case ($501 vs. $900), A is better off sharing (the best case is identical, $1000 either way). B would have the same payoff metrics for their own decision.

Thus, when maximizing the payoff to the whole, sharing is always the better decision. If both A and B are rational players, they would both share, and $800 is the result.

Now let's look at what would happen if our objective was to maximize our OWN payoff instead of the total.

The payoff matrix (for team A) is:
A shares, B doesn't - $0
B shares, A doesn't - $1000
A shares, B shares - $400
Neither shares - $1

If A shares, the best case is $400, the worst case is $0, and the EV is $200.

If A doesn't share, the best case is $1000, the worst case is $1, and the EV is $500.50.

In this scenario, not sharing is the best choice. So A and B, both being rational, choose not to share and each gets $1.

---------------

Notice how when the objective is to maximize the "greater good", each team walks away with $400. But when the objective is to maximize your OWN payoff, each team only walks away with $1.

GP isn't just a good idea, it's mathematically optimal.
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Unread 06-08-2009, 07:52 PM
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Re: Funding Dilema (game)

First off, I'd share. Regardless of the other cause. It just seems right. IF I am required to stick to the rules.

However, I think I'd turn down the company as a sponsor in the real world. Simply, if they are going to attempt to pit two charities(pretty well what we all are) against each other, I don't want their name on my bot or associated with my team.

*BONUS QUESTION*
What if it wasn't another FIRST team? What if it was the Girl Scouts? Or a BattleBots Team? What if it was an political group you disagree with?(lets not name specifics) The reason I ask, it seems a lot of the prior posts use the word IF. If it was another FIRST team, I'd.... Or I'd do .... since its another FIRST team. I want to see if your reactions would be the same, if it wasn't another FIRST team.
*BONUS QUESTION*
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Unread 06-09-2009, 07:44 AM
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Re: Funding Dilema (game)

Interesting Point Molten.

If it truly was a group that I hate (like the Girl scouts and their evil delicious cookies j/k )... I would always choose not to share. If i am truly against their ideals, then I would either want them to get 0 and me get everything, or I would be second happiest with both of us essentially geting 0 ($1)....
***********************************************
This gets a bit long winded, but not being exposed to an economics class, I found this stuff really fascinating and wanted to share. I am assuming others may get some value from this too.

Jared's post (thank you) not only explains the classic strategy for Prisoner's Dilema (the real name), but it also highlights a couple of other important things.

#1 Greater good can come from cooperation. If I was selfish and rational I wouldn't share, and neither would the other team, and thus we would end up only getting $1. If I want the best for my team, I would try to get the compromise. Superrational players would act in their own interest until they encounter another Superrational player, then they both would cooperate. Which brings us to...

#2 Communication and faith are an essential parts of cooperation. Without communication, it is blind faith (that the other FIRST team will do the "right" thing). With communication, you are still relying on faith as the other team could double cross you. Thus the importance of a moral code (via religon, faith, honor, karma, or GP philosophy).


This game is often criticized for having a lack of applicability to the real world. I would like to use a tangential example.

As long as funding is plentiful, teams are not really in competition for funding. Now that it is less plentiful, you here statements like, "I don't want FIRST spreading because that would mean less funding or mentors for my team". This is the "do what's best for yourself (rational player) and it is best for the community" strategy. This was a common economic belief for a long time (and still is in many areas). Others have proven mathematically though that cooperation can create a greater good. Think Costco memberships, MLMs, Gym memberships.... by signing up and pledging to do something as a group, the group can do and purchase things that the individuals cannot accomplish. Imagine buying an entire gyms worth of equipment to get a good workout...

Back to a FIRST example...

Say you have a state where you know funding is going to decrease by say 50% or more. Currently this state has a lot of good teams, some mediocre teams, and some teams just starting out. If the resources dried up by 50% and it was a competitive environment, then it would turn into dog eat dog and the 50% strongest and/or most cunning would survive. Now if that state had 3 regionals going, it would be reduced to 1 (can't really have 1/2 a regional, and Regionals are funded by donations). This is an ugly option. Most FIRST persons (Superrationals) would agree that a better solution would be to figure out how to share the resources as long as that means everyone is not starving. The problem is that in order for this to work, everyone has to do it. Otherwise the system would break down. In this system, the events would be smaller in production scale and thus cost, but still retain as many of the important characteristics as possible (the stuff that feeds teams).
I don't think the discussion was "Hey Superrationals are cool so what would a Superrational do in this scenario?", but I know the folks that planned things were thinking of a better group solution.

Here is the Wiki link to Prisoner's Dilema....
http://en.wikipedia.org/wiki/Prisoner's_dilemma

Read through to the economics section. The part about Cigarette companies being more profitable now that advertising is banned is counterintuitive, but makes a ton of sense once you understand the circumstances.

One important problem with the "Superrational" strategy is it looks a like like the "Nice" strategy which is also called the suckers bet. If you always share and you are surrounded by a group of Rational (selfish) players, they will eat you alive. That is why the Superrational strategy changes faces. Thus the formula for winning strategies are:
(from the Wiki-citing Axelrod):

You must be:

Nice
The most important condition is that the strategy must be "nice", that is, it will not defect before its opponent does (this is sometimes referred to as an "optimistic" algorithm). Almost all of the top-scoring strategies were nice; therefore a purely selfish strategy will not "cheat" on its opponent, for purely utilitarian reasons first.
Retaliating
However, Axelrod contended, the successful strategy must not be a blind optimist. It must sometimes retaliate. An example of a non-retaliating strategy is Always Cooperate. This is a very bad choice, as "nasty" strategies will ruthlessly exploit such players.
Forgiving
Successful strategies must also be forgiving. Though players will retaliate, they will once again fall back to cooperating if the opponent does not continue to defect. This stops long runs of revenge and counter-revenge, maximizing points.
Non-envious
The last quality is being non-envious, that is not striving to score more than the opponent (impossible for a ‘nice’ strategy, i.e., a 'nice' strategy can never score more than the opponent).

Nice, Retaliating, Forgiving, Non-envious.... Sounds like a lot of moral codes I know.....
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Unread 06-10-2009, 02:30 PM
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Re: Funding Dilema (game)

Quote:
Originally Posted by Chris is me View Post
The Prisoner's Dilemma, but applied to FIRST.

In this case, I wouldn't take their money. They're financially rewarding sabotage, and encouraging acts that would make no one's grandmother proud. I wouldn't judge the other team for being desperate for cash, though. They might need more than $400 and be out of options, and it would be unfair of me to think of them as un-GP...

If you're going to deny a FIRST team money based on one of the teams being extremely GP, the sponsor clearly doesn't get FIRST, and I want none of their money.

If the sponsor secretly would give neither team money unless they both shared, now that would be different. A valuable lesson rather than manipulation.
If the money's green, I'm not turning it away!
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Unread 06-10-2009, 09:46 PM
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Re: Funding Dilema (game)

A solution I just thought of:

Why not say no to the money, and if they agreed to share, you give them half?
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Unread 06-10-2009, 09:49 PM
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Re: Funding Dilema (game)

Quote:
Originally Posted by Chris is me
Why not say no to the money, and if they agreed to share, you give them half?
I don't know. There really isn't a rule put in for if you just refuse to take any money. Would the team that didn't refuse get $1000 or less?
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Unread 06-10-2009, 10:06 PM
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Re: Funding Dilema (game)

Sorry, I meant say no to sharing.
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Unread 06-11-2009, 07:59 AM
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Re: Funding Dilema (game)

Quote:
Originally Posted by Mr. Pockets View Post
I don't know. There really isn't a rule put in for if you just refuse to take any money. Would the team that didn't refuse get $1000 or less?
Great observation Chris:
I think that is what Chris is getting at. If we both share, we get $400 each. If I don't share, and you share, I get $1000, but I will give you $500. This premise would work, but would require communication and trust. You would not only have to communicate with the other team, and have them trust you that you will not double cross, but then you may have to communicate with your school to explain why the funding you recieved really needs to go in part to another team.
Lesson: With intelligence, excellent communication, and a little faith, more is possible than with just an altruistic mindset and faith alone.


*****************
Slight tangent:

Ayn Rand wrote a lot about the virtues of selfishness, and the inherent evil in charity. At the time collectivism and communism were running rampant. These are real concerns that have a lot of people worried today. How can charity be bad? For example, feeding the bears at Yellowstone seems like a nice and good thing to do until someone decides not to feed the bears, and then is attacked by the bears because the bears want to enforce GP . (this is a bit of a tasteless joke so GP Police go easy on me). There are a lot of other examples like that. Rand's books often cover scenarios where economic engines are ground to a halt due to "good intentions". It is an interesting contrast to what we are normally taught, and often can make people purely disbelieve in the virtues of charity.

In reality, there is a delicate balance. Working for a common good is usually noble and altruistic, but it also makes you more vulnerable to scammers and persons wanting to cheat "the system". Those that believe in the virtues of charity and common good will call the cheating a worthy expense for the overall good. Those that oppose it will site it as wasted resource that will eventually lead to a greater worse. Those with a balanced view will recognize the good being done, and work on solutions to minimize the waste and cheating.
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