|
|
| Line 1: |
Line 1: |
| In [[game theory]], the '''traveler's dilemma''' (sometimes abbreviated '''TD''') is a type of non-[[zero-sum]] game in which two players attempt to maximize their own payoff, without any concern for the other player's payoff.
| |
|
| |
|
| The game was formulated in 1994 by [[Kaushik Basu]] and goes as follows:<ref>[[Kaushik Basu]], "The Traveler's Dilemma: Paradoxes of Rationality in Game Theory"; ''American Economic Review'', Vol. 84, No. 2, pp. 391–395; May 1994.</ref><ref>Kaushik Basu,[http://www.scientificamerican.com/article/the-travelers-dilemma/ "The Traveler's Dilemma"]; ''Scientific American Magazine'', June 2007</ref>
| |
|
| |
|
| ''An airline loses two suitcases belonging to two different travelers. Both suitcases happen to be identical and contain identical items. An airline manager tasked to settle the claims of both travelers explains that the airline is liable for a maximum of $100 per suitcase (he is unable to find out directly the price of the items), and in order to determine an honest appraised value of the antiques the manager separates both travelers so they can't confer, and asks them to write down the amount of their value at no less than $2 and no larger than $100. He also tells them that if both write down the same number, he will treat that number as the true dollar value of both suitcases and reimburse both travelers that amount. However, if one writes down a smaller number than the other, this smaller number will be taken as the true dollar value, and both travelers will receive that amount along with a bonus/malus: $2 extra will be paid to the traveler who wrote down the lower value and a $2 deduction will be taken from the person who wrote down the higher amount. The challenge is: what strategy should both travelers follow to decide the value they should write down?'' | | Il ya maintenant de nombreux imitateurs, mais aucun d'entre eux sont enus pr��s d'��galer, et encore moins d��passer, comme la marque ghd meilleurs et les plus fiables redresseurs dans le monde��friser les cheeux GHD terre reste maintenant. Et il est acceptable pour les c��l��brit��s au public admis. il est de la plus haute importance de maintenir la prudence quand stylers GHD IV en ligne. ��termination des sylers GHD faux ou faux peut facile si ous donner le temps de ous-m��me. |
|
| |
|
| One might expect a traveler's optimum choice to be $100; that is, the traveler values the antiques at the airline manager's maximum allowed price. Remarkably, and, to many, counter-intuitively, the traveler's optimum choice (in terms of [[Nash equilibrium]]) is in fact $2; that is, the traveler values the antiques at the airline manager's ''minimum'' allowed price.
| | Les gens dans la h?te font toujours une erreur et aussi ceux sont deiennent d��sesp��r��s pour obtenir la chose instantan��ment aussi sont agress��es parce qu'ils ne font pas attention �� la petite de peu d'informations qui peuent les emp��cher d'��tre abandonn��. Rappelez-ous que tous ces articles faux sont principalement endus �� traers diff��rents sites d'ench��res comme eBay, BIC, mais ous ne pouiez pas r��pondre parce que ous n'aez pas know. |
|
| |
|
| For an understanding of this paradoxical result, consider the following rather whimsical ''proof''.
| | Yes, il est ��tonnant de faire d��frisage que ous pouez sentir otre cheeux raides et d��licieux sans noeuds pendant heures utilisant GHD cheeux machine �� dresser. GHD indulgence pourpre: La nouelle tendance Il ya des couleurs ��tonnantes lib��r��s aec cette machine �� dresser les cheeux GHD et le dernier est indulgence iolet qui a s?rement faire os amis erts de jalousie! C'est exactement ��ident de choisir l'��dition pourpre de redresseurs GHD car il est la marque de la nouelle d��claration de cheeux et le style. |
|
| |
|
| *Alice, having lost her antiques, is asked their value. Alice's first thought is to quote $100, the maximum permissible value.
| | les actiit��s de R de Formule ont pris place dans un grand parking tout un lot ou dans les rues de m��tropole. Aec stockcar course, l'article est �� compl��ter pour commencer aec l'emplacement. Ce n'est raiment pas le cas aec la m��thode . Comme auparaant mentionn��, 'aance il s'a��re sous la forme d'absolution ce moment inoubliable pour tous les ��tres humains aec prise belstaff apparition affection compte tenu de l'apparition de GHD MK. |
| *On reflection, though, she realizes that her fellow traveler, Bob, might also quote $100. And so Alice changes her mind, and decides to quote $99, which, if Bob quotes $100, will pay $101.
| |
| *But Bob, being in an identical position to Alice, might also think of quoting $99. And so Alice changes her mind, and decides to quote $98, which, if Bob quotes $99, will pay $100. This is greater than the $99 Alice would receive if both she and Bob quoted $99.
| |
| *This cycle of thought continues, until Alice finally decides to quote just $2—the minimum permissible price.
| |
|
| |
|
| Another proof goes as follows:
| | GHD MK d��frisage fer est tout simplement incroyable et absolument pourrait ��tre l'absolution de la science. Aec plus d'affection ceux-ci ont appara?tre comme un bienfait pour aider s'acclimater les collines inflexibles. Il est na?ement incroyable et ous ne pouez pas appr��hender �� moins obtenir un pour ous personnellement. Aec plusieurs apparitions aantageuses, Il ya moins de graisse suppl��mentaire et les bact��ries qui p��n��trent dans le corps qui peut prooquer des maladies cardiaques et les infections. |
| *If Alice only wants to maximize her own payoff, choosing $99 trumps choosing $100. If Bob chooses any dollar value 2–98 inclusive, $99 and $100 give equal payoffs; if Bob chooses $99 or $100, choosing $99 nets Alice an extra dollar.
| |
| *A similar line of reasoning shows that choosing $98 is always better for Alice than choosing $99. The only situation where choosing $99 would give a higher payoff than choosing $98 is if Bob chooses $100—but if Bob is only seeking to maximize his own profit, he will always choose $99 instead of $100.
| |
| *This line of reasoning can be applied to ''all'' of Alice's whole-dollar options until she finally reaches $2, the lowest price.
| |
|
| |
|
| The ($2, $2) outcome in this instance is the Nash equilibrium of the game. However, when the game is played experimentally, most participants select the value $100 or a value close to $100, including both those who have not thought through the logic of the decision and those who understand themselves to be making a [[Rational choice theory|non-rational choice]].{{Citation needed|date=October 2011}} 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. These experiments (and others, such as [[focal_point_(game_theory)|focal points]]) show that the majority of people do not use purely rational strategies, but the strategies they do use are demonstrably optimal. This paradox has led some{{Weasel-inline|date=August 2011}} to question the value of game theory in general, while others have suggested that a new kind of reasoning is required to understand how it can be quite rational ultimately to make non-rational choices. For instance, Capraro has proposed a model where humans do not act a priori as single agents but they forecast how the game would be played if they formed coalitions and then they act so as to maximize the forecast. His model fits the experimental data on the Traveler's dilemma and similar games quite well. <ref name = Capraro>{{cite journal | last1=Capraro | first1= V | year=2013 | title=A Model of Human Cooperation in Social Dilemmas |journal=PLoS ONE | volume=8 | issue=8 | pages=e72427 | doi=10.1371/journal.pone.0072427 | url=http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0072427 }}</ref>
| | Vous ��tes capable de oir la iande amant ballonnement et obtenir des mati��res grasses, m��me si la pr��seration de otre propre corps sain aec le ��g��tarisme. Apr��s aoir proclam�� que ous mangez plus sain aec le ��g��tarisme, ous ous sentiriez les non-croyants ont quitter ��coute ous. Le dernier serice de recyclage pour frapper le march�� semble ��tre pour redresseurs d��fectueux ou ieux cheeux GHD. Aouons-le, nous ne probablement pas besoin de ou paires de rechange, et un ensemble d��fectueux de GHD n'est pas utile �� personne. |
|
| |
|
| One variation of the original traveler's dilemma in which both travelers are offered only two integer choices, $2 or $3, is identical mathematically to the [[Prisoner's dilemma]] and thus the traveler's dilemma can be viewed as an extension of prisoner's dilemma. The traveler's dilemma is also related to the game [[Guess 2/3 of the average]] in that both involve deep [[Strategic dominance#Iterated_elimination_of_dominated_strategies_.28IEDS.29|iterative deletion of dominated strategies]] in order to demonstrate the Nash equilibrium, and that both lead to experimental results that deviate markedly from the [[Game theory|game-theoretical]] predictions.
| | La plupart des filles que je connais ont ��clabouss�� sur une nouelle fantaisie IV redresseur en rose, ous ous retrouerez aec GHD d��frisants sans garantie, GHD ne ous donnera pas le moment de la journ��e.<br><br>If you beloved this write-up and you would like to get much more data concerning [http://tinyurl.com/llahzns Lisseur ghd] kindly visit the web site. |
| | |
| ==Payoff matrix==
| |
| The canonical [[payoff matrix]] is shown below (if only integer inputs are taken into account):
| |
| | |
| {| class="wikitable"
| |
| |+ Canonical TD payoff matrix
| |
| |
| |
| !scope="col" style="color: #900"|100
| |
| !scope="col" style="color: #900"|99
| |
| !scope="col" style="color: #900"|98
| |
| !scope="col" style="color: #900"|97
| |
| !scope="col" style="color: #900"|⋯
| |
| !scope="col" style="color: #900"|3
| |
| !scope="col" style="color: #900"|2
| |
| |-
| |
| !scope="row" style="color: #009"|100
| |
| |<span style="color: #009">100</span>, <span style="color: #900">100</span>
| |
| |<span style="color: #009">97</span>, <span style="color: #900">101</span>
| |
| |<span style="color: #009">96</span>, <span style="color: #900">100</span>
| |
| |<span style="color: #009">95</span>, <span style="color: #900">99</span>
| |
| |⋯
| |
| |<span style="color: #009">1</span>, <span style="color: #900">5</span>
| |
| |<span style="color: #009">0</span>, <span style="color: #900">4</span>
| |
| |-
| |
| !scope="row" style="color: #009"|99
| |
| |<span style="color: #009">101</span>, <span style="color: #900">97</span>
| |
| |<span style="color: #009">99</span>, <span style="color: #900">99</span>
| |
| |<span style="color: #009">96</span>, <span style="color: #900">100</span>
| |
| |<span style="color: #009">95</span>, <span style="color: #900">99</span>
| |
| |⋯
| |
| |<span style="color: #009">1</span>, <span style="color: #900">5</span>
| |
| |<span style="color: #009">0</span>, <span style="color: #900">4</span>
| |
| |-
| |
| !scope="row" style="color: #009"|98
| |
| |<span style="color: #009">100</span>, <span style="color: #900">96</span>
| |
| |<span style="color: #009">100</span>, <span style="color: #900">96</span>
| |
| |<span style="color: #009">98</span>, <span style="color: #900">98</span>
| |
| |<span style="color: #009">95</span>, <span style="color: #900">99</span>
| |
| |⋯
| |
| |<span style="color: #009">1</span>, <span style="color: #900">5</span>
| |
| |<span style="color: #009">0</span>, <span style="color: #900">4</span>
| |
| |-
| |
| !scope="row" style="color: #009"|97
| |
| |<span style="color: #009">99</span>, <span style="color: #900">95</span>
| |
| |<span style="color: #009">99</span>, <span style="color: #900">95</span>
| |
| |<span style="color: #009">99</span>, <span style="color: #900">95</span>
| |
| |<span style="color: #009">97</span>, <span style="color: #900">97</span>
| |
| |⋯
| |
| |<span style="color: #009">1</span>, <span style="color: #900">5</span>
| |
| |<span style="color: #009">0</span>, <span style="color: #900">4</span>
| |
| |-
| |
| |⋮
| |
| |⋮
| |
| |⋮
| |
| |⋮
| |
| |⋮
| |
| |⋱
| |
| |⋮
| |
| |⋮
| |
| |-
| |
| !scope="row" style="color: #009"|3
| |
| |<span style="color: #009">5</span>, <span style="color: #900">1</span>
| |
| |<span style="color: #009">5</span>, <span style="color: #900">1</span>
| |
| |<span style="color: #009">5</span>, <span style="color: #900">1</span>
| |
| |<span style="color: #009">5</span>, <span style="color: #900">1</span>
| |
| |⋯
| |
| |<span style="color: #009">3</span>, <span style="color: #900">3</span>
| |
| |<span style="color: #009">0</span>, <span style="color: #900">4</span>
| |
| |-
| |
| !scope="row" style="color: #009"|2
| |
| |<span style="color: #009">4</span>, <span style="color: #900">0</span>
| |
| |<span style="color: #009">4</span>, <span style="color: #900">0</span>
| |
| |<span style="color: #009">4</span>, <span style="color: #900">0</span>
| |
| |<span style="color: #009">4</span>, <span style="color: #900">0</span>
| |
| |⋯
| |
| |<span style="color: #009">4</span>, <span style="color: #900">0</span>
| |
| |<span style="color: #009">2</span>, <span style="color: #900">2</span>
| |
| |}
| |
| | |
| Denoting by <math>S = \{2,...,100\}</math> the [[Strategy (game theory)#Strategy_set|set of strategies]] available to both players and by <math>F: S \times S \rightarrow \mathbb{R}</math>
| |
| the [[Normal-form_game#General_formulation|payoff function]] of one of them we can write | |
| :<math>F(x,y) = \min(x,y) + 2\cdot\sgn(y-x)</math>
| |
| (Note that the other player receives <math>F(y,x)</math> since the game is [[Symmetric_game|quantitatively symmetric]]).
| |
| | |
| ==References==
| |
| <references/>
| |
| | |
| {{Game theory}}
| |
| [[Category:Game theory]]
| |
| [[Category:Dilemmas]]
| |
Il ya maintenant de nombreux imitateurs, mais aucun d'entre eux sont enus pr��s d'��galer, et encore moins d��passer, comme la marque ghd meilleurs et les plus fiables redresseurs dans le monde��friser les cheeux GHD terre reste maintenant. Et il est acceptable pour les c��l��brit��s au public admis. il est de la plus haute importance de maintenir la prudence quand stylers GHD IV en ligne. ��termination des sylers GHD faux ou faux peut facile si ous donner le temps de ous-m��me.
Les gens dans la h?te font toujours une erreur et aussi ceux sont deiennent d��sesp��r��s pour obtenir la chose instantan��ment aussi sont agress��es parce qu'ils ne font pas attention �� la petite de peu d'informations qui peuent les emp��cher d'��tre abandonn��. Rappelez-ous que tous ces articles faux sont principalement endus �� traers diff��rents sites d'ench��res comme eBay, BIC, mais ous ne pouiez pas r��pondre parce que ous n'aez pas know.
Yes, il est ��tonnant de faire d��frisage que ous pouez sentir otre cheeux raides et d��licieux sans noeuds pendant heures utilisant GHD cheeux machine �� dresser. GHD indulgence pourpre: La nouelle tendance Il ya des couleurs ��tonnantes lib��r��s aec cette machine �� dresser les cheeux GHD et le dernier est indulgence iolet qui a s?rement faire os amis erts de jalousie! C'est exactement ��ident de choisir l'��dition pourpre de redresseurs GHD car il est la marque de la nouelle d��claration de cheeux et le style.
les actiit��s de R de Formule ont pris place dans un grand parking tout un lot ou dans les rues de m��tropole. Aec stockcar course, l'article est �� compl��ter pour commencer aec l'emplacement. Ce n'est raiment pas le cas aec la m��thode . Comme auparaant mentionn��, 'aance il s'a��re sous la forme d'absolution ce moment inoubliable pour tous les ��tres humains aec prise belstaff apparition affection compte tenu de l'apparition de GHD MK.
GHD MK d��frisage fer est tout simplement incroyable et absolument pourrait ��tre l'absolution de la science. Aec plus d'affection ceux-ci ont appara?tre comme un bienfait pour aider s'acclimater les collines inflexibles. Il est na?ement incroyable et ous ne pouez pas appr��hender �� moins obtenir un pour ous personnellement. Aec plusieurs apparitions aantageuses, Il ya moins de graisse suppl��mentaire et les bact��ries qui p��n��trent dans le corps qui peut prooquer des maladies cardiaques et les infections.
Vous ��tes capable de oir la iande amant ballonnement et obtenir des mati��res grasses, m��me si la pr��seration de otre propre corps sain aec le ��g��tarisme. Apr��s aoir proclam�� que ous mangez plus sain aec le ��g��tarisme, ous ous sentiriez les non-croyants ont quitter ��coute ous. Le dernier serice de recyclage pour frapper le march�� semble ��tre pour redresseurs d��fectueux ou ieux cheeux GHD. Aouons-le, nous ne probablement pas besoin de ou paires de rechange, et un ensemble d��fectueux de GHD n'est pas utile �� personne.
La plupart des filles que je connais ont ��clabouss�� sur une nouelle fantaisie IV redresseur en rose, ous ous retrouerez aec GHD d��frisants sans garantie, GHD ne ous donnera pas le moment de la journ��e.
If you beloved this write-up and you would like to get much more data concerning Lisseur ghd kindly visit the web site.