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centipede game

The article states that this is an extension of PD. I don't see it in the SA article, but would it be inappropriate to say that this is a variant of the centipede game? Smmurphy^(Talk) 02:51, 23 May 2007 (UTC)[reply]

It does bear a strong similarity to the centipede game, except the centipede game has more than one Nash equilbria (but only one subgame perfect equilibrium), while this game has only one NE. This game also has some similarity to Guess 2/3 of the average in that it involves deep iterative deletion of dominated strategies in order to demonstrate the NE. I think its okay to say it's similar to the PD. The socially optimal strategy in this game is not an NE, while dominance reasoning leads individuals to a very inoptimal outcome (like the PD). --best, kevin [kzollman][talk] 20:29, 23 May 2007 (UTC)[reply]

Not an extension of Prisoner's Dilemma

The article stated that TD was an extension of PD if you are limited to 2 distinct numbers. This is incorrect. In PD, the temptation to defect is greater than the reward for cooperation. If you are limited to 2 and 100 as your only options, the temptation to defect is 4, and the reward for cooperation is 100. This would result in 2 Nash Equilibrii, and thus not a prisoner's dilemma. -Todd(Talk-Contribs) 00:46, 10 June 2007 (UTC)[reply]

Indeed. Have re-formulated how this game is linked to PD. (see article) JocK 11:25, 10 June 2007 (UTC)[reply]

Style

What is the general consensus about when or how to capitalize Traveler's Dilemma, Prisoner's Dilemma, Nash's Equilibrium etc. I see it both ways but usually capitalizing both words like any other proper noun. I think all the WP game theory articles should use consistent style throughout on these names. Venado 23:36, 15 June 2007 (UTC)[reply]

Confused by word "deep" for IEDS

I have never heard the term deep used for iterative elimination of dominated strategies. Should it be explained or references identified?Venado 00:02, 16 June 2007 (UTC)[reply]

A deep iteration is an iteration that is applied many times. Perhaps there is a better word, but can't think of any.JocK 06:53, 16 June 2007 (UTC)[reply]

I think it better to leave off the word unless the term "deep iteration" is perhaps described through link etc. Isn't the number of iterations to be performed simply determined by the number of choices available? Classic TD is max $100 but Basu describes variant of TD played with only 2 choices.Venado 14:11, 16 June 2007 (UTC)[reply]

The large number of iterations needed to reach the NE (in TD indeed related to the number of strategic choices) is key to the fact that in TD (and also in 'guess 2/3 of the average') real-life experiments (including real-money experiments) result in strong deviations from the game-theoretical solution. Would therefore not like to see the word 'deep' disappear. JocK 17:41, 16 June 2007 (UTC)[reply]

Thank you. I think your article edit now explains its meaning much more clearly. Venado 15:04, 17 June 2007 (UTC)[reply]

Meaning of non-rational

The article includes "as well as those who understand themselves to be making a non-rational choice. Furthermore, the travelers are rewarded by deviating strongly from the Nash equilibrium in the game and obtain much higher rewards than would be realized with the purely rational strategy." and "others have suggested that a new kind of reasoning is required to understand how it can be quite rational ultimately to make nonrational choices"

I think nonrational is being used with a specific meaning that isn't the same as most people would expect and I think this should be avoided if at all possible. I don't know the litrature but I would have thought we should be saying something more like:

"... as well as those who understand themselves to be making a decision which deviates from the Nash equilibrium. This policy to deviate from the Nash equilibrium is perfectly rational if you believe you have reason to believe the assumptions made in arriving at the Nash equilibrium do not apply. It is possible that there are many ways to see a flaw in the Nash equilibrium solution but one follows as an example:

If a player chooses 99 and if the other player knows this strategy then this strategy is dominated by a strategy that chooses 98. The second 'if' does not apply; the other player does not know the first's strategy. The Nash equilibrium follows as if players know each others strategy but they do not.

...others have suggested that a new kind of reasoning is required to understand how it can be quite rational ultimately to make choices that deviate from the Nash equilibrium solution."

I am still not sure about that last sentence is a new reasoning required or has such a new reasoning been suggested? (I can't be the first to suggest something as obvious as above.) crandles 12:32, 8 August 2007 (UTC)[reply]

The start of the article should be a clue, "In game theory." The meaning of "rational" is the meaning it has in game theory. You are right that perhaps it should be explained, but the word shouldn't be changed, because it has a very specific meaning (see rational choice theory and preference). Also, please be careful of original research. Best, Smmurphy^(Talk) 15:34, 8 August 2007 (UTC)[reply]

I have (as an interim step) editted in a link to indicate the specific meaning. That doesn't mean I think that is adequate to address the concerns I raised. The start of the article may well be a clue and while, I didn't need that clue, I don't think that is enough. The purpose of an encyclopedia is not to just explain to those who already understand - that would make encyclopia useless. You seem to agree that non-rational has a specific meaning and is easily misunderstood. So is that acceptable? I suggest not. If not, do you reword to avoid that term like I have shown is possible or do you use the term with added explanation?

I agree original research should not be added. (Note that I said 'something like' rather than editing in that paragraph.) However there must be something in the litrature that suggests why/where the assumptions in (correctly) deducing the Nash equilibrium solution are not a correct reflection of reality in such a way that the Nash equilibrium solution is not an optimum strategy for a human playing the game in the real world. I suggest that needs to be added to the article. Note that the article is titled "Traveler's dilemma" not "The Nash equilibium solution to Traveler's dilemma". crandles 16:48, 8 August 2007 (UTC)[reply]

You are right about jargon, we should be more clear, although I don't think we should remove the word, as that could actually make it less clear to someone familiar with GT. I fully agree with your point that we should explain why we care about certain equilibrium in the articles. Generally, people studying game theory are asked to find NE or SPE or whatever is appropriate in any game they think up, and often the motivation of why those equalibria are sought is lost. Also, those equilibria are not always intuitive, and other equilibria might be suggested for particular games that make more sense. I promise I'll find the time to try to bring in some alternative equalibria and, if relevant, empirical support for one or another (both here and Centipede game - let me know or bring a note to Wikiproject:Game Theory know if you have an issue with a GT article and no one addresses it). I do not agree with you that Basu's application of the NE concept is incorrect, I'm not sure where to start, except to point to Nash equilibrium. As for the literature, I've only read the SA article, but I can search JSTOR and google scholar as well as anyone, and again I promise to poke around a bit soon. By the way, if you (crandles) have any general GT questions, feel free to email me. Best, Smmurphy^(Talk) 05:09, 9 August 2007 (UTC)[reply]

This dilemma is retarded. It assumes the premise is to get 'more' money than the other player, whereas people's actual base premise, probably on an evolutionary level, is to go for maximum gain. If you want maximal personal gain, without consideration towards your 'competitor' then your best choice is between $98 and $100. If they renamed the money, say 'snoods', and told people that the aim is NOT to get the most snoods possible, in fact you don't even care about snoods, but that the goal is to get more 'snoods' than the competitor, then more people might go for the $2 option. But even so, this tactic in the normal world is so usually associated with a heavy desire for say, vengeance or competitiveness above all other considerations, that most people would be unlikely to pursue this tactic, as it is not usually maximally beneficial. - Sangrail. —Preceding unsigned comment added by 222.154.238.36 (talk) 03:56, 30 January 2008 (UTC)[reply]

You misunderstand the purpose of game theory. Prisoner's Dilemma isn't a useful theory because prisoner's actually have such a dilemma, but because the concepts behind it abstract to many other situations. Likewise, the potential usefulness of this theory isn't limited to playing a game with some bizarre rules. Also, you haven't thought through all of the implications of the game. If you are trying to maximize the amount of money you will take in, there is no reason to choose $100; if your opponent chooses $100, you will make $101 by choosing $99, rather than $100 for choosing $100; if you opponent chooses $99, then you make $99 instead of the $97 you would make for choosing $100; for every other number value there is no difference for choosing $99 vs $100, so naturally, $99 is strictly better for you profit-wise than $100. Similarly, there is no reason for your opponent to choose $100 either, as he will be strictly better off choosing $99. If both of you figure that out, then you should also both realize that there is no reason to choose $99 either for the same reason as $100. You can make similar realizations all the way down to $2. -Todd(Talk-Contribs) 13:01, 31 January 2008 (UTC)[reply]

I Don't Get It / Show Work For The Rational Strategy

I don't understand how the rational strategy can get down so low; perhaps someone has a non-OR showing of work? In any case, here's an OR analysis trying to find the most rational strategy, hopefully somebody can correct it, even if with OR, and we can find earmarks of a solution:

First, consider three assumption meta-strategies for the other traveler: mimicry(use the same strategy I do for the same reasons) vs anticipation(assume he'll correctly guess my strategy and optimize his strategy to a possibly-different value) vs random(assume he fails with game theory, and picks some other number). If I assume he's mimicking, our choices will be equal, and therefore my payoff will be equal to my choice. I should generally maximize my choice. This assumption leads to the specific choice of 100$. If I assume he's anticipating, he'll successfully undercut me for the undercut bonus(and to avoid the overcut penalty), and therefore my payoff will be 2$ less than his choice. I should generally maximize his choice. Since in this case his choice will simply be upper-bounded by my choice, in order to maximize his choice I should maximize my choice. This assumption also leads to the specific choice of 100$. If I assume he's choosing randomly, my payoff will be simply upper-bounded by my choice, but then adds what I can gain from the undercut bonus(and from avoiding the overcut penalty). Getting the undercut bonus instead of the overcut penalty has a relative payoff of 4$, so my minimum choice with this assumption is 96$, but the relative value of choices between 96$ and 100$ depends on the odds I determine for the undercut bonus and overcut penalty. So, the "baseline" choice is 100$, since that's a possible optimum under all assumptions; however, the random assumption could bring me down as low as 96$. All choices below 96$ are inferior, and only the random assumption offers any reason to deviate from the "baseline" strategy, so all we need to examine is how much the random assumption lowers it. 100$ is a decent choice; 99$ has a cost of up to 1$, and offers 2$ after that in the case of two specific choices(it removes the overcut penalty for his choice of 99$, and gains the undercut bonus for his choice of 100$). 98$ has a cost of up to 2$, and offers 2$ in two cases and 4$ in one case(it gains the undercut bonus for his choice of 100$, which is a wash, it removes the overcut penalty for his choice of 98$, which is also a wash, and it replaces the overcut penalty with the undercut bonus for his choice of 99$, for a net payoff increase of 2$ in one choice). Assuming an even random spread, 99$ offers twice the payoff increase of 98$; 97$ doesn't even come close. If his specific choice of 99$ were likely enough under the random assumption, then the random assumption could optimize to 98$, but in all other cases, 99$ is preferable. So the answer is 99$ if you consider the random assumption sufficiently compelling, 100$ otherwise.

So what am I doing wrong? Is the cost of a strategy not normally considered as part of rational play? And if so, why? Darekun (talk) 09:50, 6 February 2008 (UTC)[reply]