What is Digg?72 Comments
- lucidguru, on 05/15/2008, -6/+25The best strategy is to cooperate up until the end and then compete and steal the last round. The problem is that you don't know when that last round will come. Cooperation is the most profitable way to go. Competing every round gets you 5 to start but only 1 after every round. And alternating between competing and cooperating gets you 2.5 per round.
- quomen, on 05/15/2008, -0/+15John Nash didn't create the Game Theory, he came up with the "Nash Equilibrium" which is the point where neither of two players of a game have anything to gain from changing their strategy. You were close though. lol basic econ coming to digg ftw.
- centerblack, on 05/15/2008, -1/+17Always cooperate.
- Conway, on 05/15/2008, -1/+12http://en.wikipedia.org/wiki/Prisoner%27s_dilemma
- digghasnoethics, on 05/15/2008, -0/+7It was called "Tit for Tat" on the programme I saw. Multiple simulation runs between different strategies showed that this one was the best out of those tested. International commerce could be said to run by the same strategy.
- Jektal, on 05/15/2008, -0/+7Yeah, as I remember it, the "tit for tat" strategy is basically:
By default: Cooperate. If they try to rob you, rob them back, if they switch back to cooperating, do the same. - centerblack, on 05/15/2008, -0/+8At least for this game, the AI waits for you to defect first.
- rlray216, on 05/15/2008, -2/+8This is awesome. Best submission of the day, IMO.
- Mejogid, on 05/15/2008, -0/+6Except it's not about getting more than the "AI" - it's about getting the greatest possible number of coins. It's not possible to get less than a tit-for-tat strategy - the worst you can do is draw.
- bobotheking, on 05/15/2008, -1/+7Have fun with your 14 gold coins. In the meantime, I will be enjoying my 42.
- quomen, on 05/15/2008, -6/+12The dominant strategy is actually to compete. The problem with your idea is that, even in a game where the player knew how many rounds they were going to play, they are going to try predict the actions of another person. Supposed that you are trying to play nice with your competitor so that you can trick them in the last round. How do you know that the competitor won't do the same thing too? You don't, so most likely he is thinking of that strategy. What's the next best idea? Maybe try to trick the person in round 9, instead of round 10 (the last one), because you're trying to predict what they are going to do. However, he would do that too and also compete in round 9. This can go on forever. However, the more rounds you have, the more likely you'll both come to an [unspoken] collusive agreement. This has been played out in millions of economics experiments.
- auto98, on 05/15/2008, -0/+5actually the best strategy is to cooperate first time, then after that do what your opponent did the time before (tit for tat as stated above)
Obviously this is assuming there is no teams or whatnot - sononame, on 05/15/2008, -1/+7Is this this John Nash's Game Theory?
- pugs909, on 05/15/2008, -1/+6did you try always competing vs this AI which uses the tit-for-tat strategy, genius?
- pugs909, on 05/15/2008, -0/+4tit for tat
- amdahlj, on 05/15/2008, -2/+5Tit for tat is the foundation of all the best strategies in iterated pd. If it isn't iterated, always defect.
- isntreal, on 05/15/2008, -1/+4tit for tat
- celticspringers, on 05/15/2008, -0/+2"that´s not how human minds work"
Really? I think there are a number of factors that incentivise co-operation in repeat PD games.
1) Reciprocal altruism: There is an opportunity for making one’s choices conditional on those of one’s partner – threatening defection in return for defection. It is rational to resist temptations to defect rather than face the damage of long term mutual non-cooperation. This is Axelrod´s fundamental argument.
2) Evolutionary psychology has shown that human behaviour is better understood in terms of strong reciprocity: we have a hard-wired predisposition to cooperate, a throwover from our hunter-gatherer evolution.
3) Reputation ( i.e. to threaten dire consequences or future benefits). Creates a presumption of credible threats.
Of course, in PD games, the ending must be unknown to both parties otherwise backward induction (where players know there is no incentive to cooperate) will unravel strategic incentives back to the beginning. But I think rational choice assumptions of behaviour are very limited. - zephc, on 05/15/2008, -2/+5There are two kinds of people: sheep and sharks. Anyone who's a sheep is fired. Who's a sheep? Sharks are winners and they don't look back 'cause they don't have necks. Necks are for sheep.
- Future2, on 05/20/2008, -0/+2quomen you're right that if this game was played once the NE is don't cooperate, and the payoffs would be (1,1). This is the nature of a PD game. When PD games are iterated though, trigger strategies (eg: tit-for-tat) can form a NE. Whether or not the trigger strategy forms a NE is dependent on the discount factor of both players. This game assumes a discount factor of 1 for both players (each round is worth the exact same as the previous).
- mirot, on 05/15/2008, -4/+8The best strategy is to first cooperate, and then copy what your opponent did on the previous round.
- Flashman, on 05/15/2008, -0/+3Is there a version of this online where we can play against one another?
- Narpas, on 05/18/2008, -0/+2Why are we prisoners in the first place? Cooperate until the very end, then mug Serendip and take all his coins. Presto! 6 coin average!
- Tanath, on 05/15/2008, -0/+2Actually, if you predict the end too soon, and defect, then it's better to alternate with a player using tit-for-tat.
- zephc, on 05/16/2008, -0/+2Jeez, its a Futurama quote, Poindexter.
- solistus, on 05/17/2008, -0/+2Tit-for-tat has been mathematically demonstrated to be the optimal strategy for IPD (that is, prisoner's dilemma with repetition). If you always defect, a TFTer will switch to defecting too, and you both do poorly. The best any strategy can possibly do in a classic IPD scenario is tie a TFTer. This is discussed elsewhere on the linked site, if you bother to read it.
quomen repeats one of the most common game theory false assumptions. Competition is, by definition, sub-optimal. It involves consuming resources (or in this case, expected value) to take other resources in a zero-sum environment. Cooperation uses resources in ways that complement each other to increase expected value. Competition in macro-economics is an example of egoist cooperation; each agent is out to maximise gain, but game relationships between agents are based on preset frameworks of cooperation. This is why business partners accomodate each other and attempt to create a mutually beneficial partnership rather than opposing each other for potential immediate gain at every turn. If you try to "always defect" in economic exchanges, you will very quickly discover that it is a very sub-optimal aproach. In the 'real world,' where you have at least partially free associations with many potential players, the prisoner's dilemma tends toward establishing cooperative norms (e.g., rule of law and property rights to allow functioning economic exchange). - isntreal, on 05/15/2008, -1/+3I wrote this program last semester in java... I'll try to find it and make it an applet.
- roodammy44, on 05/15/2008, -0/+2Shark population = some nearing extinction
Sheep population = More sheep than humans
Looking at it like that, being aggressive is a bad strategy.
But also looking at it through evolutionary biology, tit for tat is nature's way of deciding who we should be altruistic to and who not to.
We can keep track, socially, of around 150 people who we can remember who has been bad to us in the past and who has been good.
If they have been bad, we treat them bad. If they have been good, we treat them good.
Therefore being a "social shark" will only get you misery your entire life, unless you only spend your time around people who don't know you. - Tanath, on 05/15/2008, -0/+2No, the best strategy is dependent on the game actually being played. This implementation is different from the scenario you're discussing, particularly in that it is playing a predictable strategy. The best strategy is tit-for-tat, until the end, and then defect at the end to avoid retaliation.
The interesting thing though, is that on average, across the entire span of all players, it's tit-for-tat strategy will still do better. - inactive, on 05/15/2008, -4/+5Police are known to lie about what evidence they have and being bullies. If I actually committed a crime and chose an associate for that, we would know better than being scared of them.
- fastspawn, on 05/15/2008, -0/+1Hi! I tried this interesting game. A lot of people here claim that competing is the dominant strategy. I am no economist, so I would not claim to know anything. What i did was cooperating all the way and won. My average was of course 3 coins gained thus
How does competing work since you will get only 1 coin average if both compete, or 2.5 average if computer and you alternate between compete and cooperate. - solistus, on 05/17/2008, -0/+1What are you talking about? You start by saying the dominant strategy is to compete (which is false), then you seem to conclude that the likely outcome is cooperation (which is correct).
The prisoner's dilemma is only a dilemma if you're concerned with absolute and not relative gain. The only way to have relative gain is defection, so always compete is the only strategy if relative gain is the goal (or, more likely, an entirely different decision model and incentive structure would exist in such a case that would not match that of the PD).
Given that we're concerned about absolute gain, the ONLY way that defecting at the end pays off is if you do it on the right turn and your opponent does not. Randomising the number of turns means that, unless you are confident that you will be right most of the time and never too far wrong (you lose a lot of absolute value for every turn after you defect), it's never correct to defect. If the number of turns is known, then the last round is functionally equivalent to a non-iterative PD, in which case, assuming you have no contextual knowledge to make a prediction based on, defection is correct. However, in most IPDs, this is not factored in; it's sort of an irrelevant detail of how some IPDs are formulated, which is why many theoretical applications assume an unspecified or infinite number of iterations. The point is to evaluate long-term reactive strategies. Non-iterative PD is about as strategic as non-iterative rock-paper-scissors (incidentally, iterative RPS is an unsolved game and thus far more complex than IPD ; ). - YourDoom123, on 05/16/2008, -0/+1reneges?
- quomen, on 05/15/2008, -1/+2Did you not read what I said? I said that when you play more than once you're more likely going to reach a collusive strategy. And where did you get defect from?
Edit: nvm I see it in the wikipedia article. ok then, thanks Prof. Wiki. - quomen, on 05/15/2008, -2/+4Yes, I did. I win every time.
How about you find a computer than can accurately predict the strategies of real humans (lots of them).
Don't forget the point of this game is to achieve the greatest well being for yourself, regardless of what the opponent does. "Winning" will always be achieved by picking the dominant strategy. Because it's the most dominant strategy, both competitors will most likely always pick it after the first round. This is called a Nash Equilibrium. - markdr123, on 05/24/2008, -0/+1Welcome to Game Theory!
- solistus, on 05/17/2008, -0/+1The game randomises the end turn a bit. If you miss by one, you end up gaining a slight relative advantage and no absolute advantage (you get your 5-0 and then a 1-1, so you still get 6 but deprive the other of 5). If you miss by more than one, you can maintain an increasingly small relative advantage, but you have an absolute loss (i.e., both players have less than 3/turn, but you have more than the AI). In most formulations of the PD, this is considered an undesirable outcome for both parties; the logic becomes much different if relative advantage is the goal, and always defect becomes the only viable strategy (cooperating can never provide a single point of relative gain). The more iterations, the less likely a late defection will be rewarded. I guess over infinite repetitions, the optimal strategy would be to spend a long time figuring out the probabilities of various numbers of total turns, then calculate the optimal turn to defect based on that.
- Makaveli604, on 05/15/2008, -0/+1Also: Philosophy, Political Science, and Economics use the Prisoners' Dilemma..
all first term classes of mine, was very eery. - rilus, on 05/16/2008, -0/+1Tit for tat
- Tanath, on 05/15/2008, -0/+1The best strategy depends not only on the game being played, but on the other strategies being used. If the others' strategies are predictable, that changes things. In the case of this implementation, it is sufficiently predictable, and there are superior strategies.
- jim3008, on 05/15/2008, -1/+2yup, i second that
- jprez, on 05/25/2008, -0/+1this is really dumb... same outcome everytime. lets get some god games in the playable games section
- Tanath, on 05/15/2008, -0/+1If you want some good reading & explanation behind this, I recommend The Evolution of Cooperation, by Robert Axelrod. He's the one who figured out the tit-for-tat thing (and then wrote the book about it).
- jondo85, on 05/17/2008, -0/+1Apparently that is the, or one of the best strategies for the dilemma; there was a programming contest a couple of years ago where everyone submitted their strategies - the winner always co-operated until the other player defected, then always defected.
Co-operation people! - Tanath, on 05/15/2008, -0/+1No, this isn't an indefinitely iterated game, nor is it a single iteration. The best strategy seems to be to cooperate until the end, then defect to avoid retaliation. If the computer player weren't playing a predictable tit-for-tat strategy this might not have been the case.
- lucidguru, on 05/15/2008, -1/+3Hawk vs Dove
- EatUrKids, on 05/15/2008, -0/+1"Not bad, but I'll bet you can do better."
He believes in ME!!! - badplacebo, on 09/11/2008, -0/+1Everyone that dugg you down has never been to prison. Thanks for keeping it real. Now toss my salad!
- Tanath, on 05/15/2008, -0/+1Someone's read The Selfish Gene.
- MarioSuperFam, on 05/24/2008, -0/+0This is an interesting game. I've found a strategy that works 50% of the time. If you hit the button without selecting anything, no one gets gold but the next round starts. If you have gold, though, and you press the button without choosing anything, you both go back to zero. So, all you need to do is alternate between taking the competition and doing nothing, and you'll win half the time.
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