Test your wits

Betrayal.Assuming that I'm socially short-sighted or just self-serving, if the other person cooperates my best response is to betray (I go free). If the other person betrays me, my best response is to betray them (Gives me a lesser sentence). No matter what they do, my best option is to betray them. Assuming the billionaire can detect intentionality, I drink the toxin and prepare myself for day of pain and consider my investment options. Can I intend to drink it knowing I don't have to? Yes, I simply make the decision to be honourable and keep my word. I can intend to keep my word, even if the rational thing to do would be to not, because matters of honour are not decided rationally - the human mind is capable of such acts irrationality.If the billionaire cannot detect intentionality I just lie to to the crazy old guy.

Heh, nice one. Here's my spin on it.A time traveller goes forwards in time 1 billion years looking for a suitable energy detector (aka a celestial thermometer). Not finding anything he then travels 5 light years in a random direction. No luck so he travels 40 light years in a direction at right angles to his previous direction. Here he finds a suitable celestial thermometer. He goes back in time 1 billion years and finds himself back where he started. What temperature is it?yeah, it doesn't work quite as well as the bear one, but...well...nevermind.Edited by Modulous, : No reason given.Edited by Modulous, : No reason given.Edited by Modulous, : No reason given.

I'd really like to see your working.

Only if we are using the iterated prisoner's dilemma. In the classic setup as in the OP defection dominates. From that very wiki page:

quote:

---

In this game, as in all game theory, the only concern of each individual player ("prisoner") is maximizing his/her own payoff, without any concern for the other player's payoff. The unique equilibrium for this game is a Pareto-suboptimal solution”that is, rational choice leads the two players to both play defectly even though each player's individual reward would be greater if they both played cooperately...In the classic form of this game, cooperating is strictly dominated by defecting, so that the only possible equilibrium for the game is for all players to defect. In simpler terms, no matter what the other player does, one player will always gain a greater payoff by playing defect. Since in any situation playing defect is more beneficial than cooperating, all rational players will play defect, all things being equal.

---

The wonderful thing about the iterated prisoner's dillemma is its application to the evolution of morality. According to game theorists the best strategies are generally (as per the wiki page) Nice (it will not defect before its opponent does)
Retaliating (It must sometimes retaliate.)
Forgiving (Though players will retaliate, they will once again fall back to cooperating if the opponent does not continue to play defects. This stops long runs of revenge and counter-revenge, maximizing points.)
Non-envious (not striving to score more than the opponent)Instead of Nash equilibria we deal with the related concept of Evolutionarily Stable Strategies. I see this as the best argument against the 'We all share a common sense of right and wrong because of an objective moral standard', since there need be no objective moral standard when we apply game theory: Such systems pretty much make themselves.

You seem to be attempting to describe super-rationality. Super-rationality differs from rational thinking as per Game Theory, though I've never come across the mathematician/economist divide you mention.Super-rationality is hardly such an established phenomenon that you can comfortably declare the Game Theory answer 'incorrect' in such absolute terms. Super-rationality requires that your opponent will necessarily pick the same answer as you do, which means that mixtures of defect and cooperate will never happen. Therefore the choices are Betray/Betray or Cooperate/Cooperate, and so Cooperate dominates.Personally, I think this essentially undercuts the point of the game by assuming that your opponent is super-rational (ie., knowing what your opponents strategy is (and knowing they will stick with it)) is tantamount to communication between players.And of course, a super-rational player versus a Game Theory player will always lose, unless the super-rational player can somehow establish he plays against a Game Theory player. If we say that the super-rational player is unsure about the strategy of his opponent - then things become much less clear-cut with certain judgements required about the probabilities and cooperating with a certain optimum probability. Using your phraseology: The mathematician will cooperate and come out ahead, only if he plays against a mathematician. If he plays an economist, he comes out way behind. Then they are mathematicians that haven't studied Game Theory. Merrill Flood, Melvin Dresher and Albert W. Tucker, the fathers of the prisoner's dilemma were all mathematicians and concluded 'defect' is the dominant strategy despite mutual cooperation being the optimal solution. This rather paradoxical result is the reason it has been named a dilemma and has been discussed and modified for over half a century.Granted, mathematicians may indeed conclude that the optimal solution is to both cooperate - though I'm sure economists would see that too. Not knowing what strategy your opponent is going to pick ensures that defect remains dominant according to game theory.If we play out a super-rationalist against either a game theoretician 50% of the time and a super-rationalist the other 50%. After 100 trials (with no memory, vengeance etc)The cooperator will get the sucker's payoff 50 times for 500 years in jail. He will get the cooperation reward 50 times for 25 years in jail. He has a total of 525 years in jail or 5.25 years per attempt.The defector under the same conditions will get the defection reward 50 times for 250 years and will get off 50 times for 2.5 years per attempt.Indeed, the cooperator had better hope he meets other cooperators at least 80% of the time because then he gets the suckers payoff 20 times for 200 years and the cooperation reward 80 times for for 40 years in prison and under these circumstances he will get 240 years or 2.4 years in prison per go on average.Of course, with so many cooperators the defectors still do better. They now get off 80 times and only spend time in jail 20 times for 100 years or 1 year in prison on average.

Yes. Game Theory is mathematics. Mathematics is not Game Theory. Thus one can be a mathematician and have not studied Game Theory. I listed several mathematicians who were also Game Theorists who invented the dilemma and how they pick 'defect'. Can you name any mathematicians who pick 'cooperate'? How many of them have studied Game Theory?As I said, I've never seen this economics vs mathematics divide on this issue. Mathematicians in my experience simply apply Game Theory and betray. In your opinion however, "The mathematicians are seeking a solution that reduces the entire amount of time spent in jail." - which would tell me that these particular mathematicians haven't studied game theory...unless they are using super-rationalism as justification. No, it's called a dilemma because "The unique equilibrium for this game is a Pareto-suboptimal solution”that is, rational choice leads the two players to both play defectly even though each player's individual reward would be greater if they both played cooperately.": wiki.I mean, if we assume that the object of the game is to go to prison for maximum amount of time, everything changes. If we assume the object of the game is to kill the guards and create a prisoner uprising to overthrow the shackles of oppression, then the optimum solution changes. Really there is only one game: What is the best rational strategy for any given prisoner. The answer: betray.Every mathematician agrees that betrayal is the best rational strategy. Some mathematicians argue that rational strategies aren't the way forward and we should use super-rational strategies. In which case the solution is a controversial cooperate. But you weren't talking about super-rational strategies. I have no idea what you are talking about here.The optimal solution might well be to BOTH cooperate, but you cannot communicate with the other prisoner. Since you cannot cooperate, mathematically speaking your best strategy is to betray. If they choose to betray you, the last thing you want to do is cooperate. If they choose to cooperate you can skip spending 6 months in prison by betraying them. In each and every case, betrayal gets you the best outcome. The one where we have to assume that both prisoner's are rational agents. The original and classic Prisoner's Dilemma as put forward by Game Theorists. In the post which you categorically stated was 'incorrect' I even clarified in an attempt to undercut soft complications by saying:

quote:

---

Assuming that I'm socially short-sighted or just self-serving

---

To remind us what you said

quote:

---

Incorrect. If you keep silent and they also do, you only get six months. If you betray and they also do, you get five years.

​

It is better to keep silent. This is an old puzzle. If you want, I can go through the math....

---

Now you seem to be suggesting that it isn't that I was incorrect at all, but that it depends on what game we are playing. Yes, it is an old puzzle but I haven't had the pleasure of seeing your maths that demonstrates it is better to keep silent. If you and the other prisoner are working as a team, or if you have set things up so that there are additional rewards for cooperating and penalties for betrayal, then it may be best to cooperate.But we don't have these things set up. You don't even know what the probabilities are of your opponent picking cooperate. If you choose cooperate, you are taking a huge risk of going to prison for a long time -> especially given the fact that no matter what you pick the other prisoner would be best served by betraying you, and the other prisoner knows that this is true of your position too.Can you find any websites that support your position? I can only find ones that don't and what you write intrigues me. Can you find this economists vs mathematicians study?

Feel free to provide a better one of your own. So when you said earlier that this solution was flat 'Incorrect' for selfish agents and that you could show me the maths to demonstrate that this was so, you were actually wrong? What you meant to say was 'As you say, this is the correct solution for selfish agents. However, I can use lots of words to explain why I think 'cooperate' can seen as the best option.' Sounds familiar. It's like when I said the best option is to betray "Assuming that I'm socially short-sighted or just self-serving", and then you said "Incorrect." Also, reading where assumptions are stated is very important. Yes, of course. That's why I said that the best solution for the prisoner's was to betray despite it being sub-optimal. Just like the bit you quoted said. The prisoners are placed into competition with one another resulting in a sub-optimal solution.Edited by Modulous, : No reason given.

You can play whatever game you like Rrhain. You can keep repeating you were playing a different game all you like. Whenever you are ready you may return to Message 11...the message you replied to. In Message 11 you can see how I explicitly stated the assumptions inherent in the standard Prisoner's Dilemma. They weren't exhaustive, obviously, but I think you'll find they cover the important parts and my subsequent replies should have clarified them considerably. You replied to Message 11, where I stated my assumptions, by saying "Incorrect". You have since indicated that my solution is correct given my stated assumptions, you don't need to repeat yourself eight times - a simple concession that you were actually wrong in Message 19 would suffice. Betrayal is the optimal solution for the 'subsystem', which is why it is the correct answer to the standard dilemma. It is, as you have stated, optimal for the total system (or global optimization) for them both to cooperate. Unfortunately for the poor prisoners the warden/sheriff has put them in a position where they cannot conspire to shoot for global optimization but have to shoot for the optimal solution for their immediate subsystem which turns out not to be globally optimal. Optimizing a problem's subsystems do not lead to global optimization (The Principle of Suboptimization).You insist that you were playing a game of 'find the globally optimal solution', which is rather pointless since it is stated pretty much in the game parameters but that's fine. The Prisoner's Dilemma as it is presented to everybody else in the world is all about how given the circumstances 'Defect' is what rational agents would do, despite them both knowing it is not the globally optimal solution. I find this variety more interesting than your version.You are the one who offered F. Heylighen as a suitable authority. Here's what he has to say about the Prisoner's Dilemma:

quote:

---

The problem with the prisoner's dilemma is that if both decision-makers were purely rational, they would never cooperate. Indeed, rational decision-making means that you make the decision which is best for you whatever the other actor chooses. Suppose the other one would defect, then it is rational to defect yourself: you won't gain anything, but if you do not defect you will be stuck with a -10 loss. Suppose the other one would cooperate, then you will gain anyway, but you will gain more if you do not cooperate, so here too the rational choice is to defect. The problem is that if both actors are rational, both will decide to defect, and none of them will gain anything. However, if both would "irrationally" decide to cooperate, both would gain 5 points. This seeming paradox can be formulated more explicitly through the principle of suboptimization.

---

I believe that is exactly what I was saying.Edited by Modulous, : No reason given.