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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:[1][2]
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?
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.
For an understanding of this paradoxical result, consider the following rather whimsical proof.
- Alice, having lost her antiques, is asked their value. Alice's first thought is to quote $100, the maximum permissible value.
- 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:
- 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 non-rational choice.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. 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 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 someTemplate:Weasel-inline 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. [3]
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 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-theoretical predictions.
Payoff matrix
The canonical payoff matrix is shown below (if only integer inputs are taken into account):
| 100 | 99 | 98 | 97 | ⋯ | 3 | 2 | |
|---|---|---|---|---|---|---|---|
| 100 | 100, 100 | 97, 101 | 96, 100 | 95, 99 | ⋯ | 1, 5 | 0, 4 |
| 99 | 101, 97 | 99, 99 | 96, 100 | 95, 99 | ⋯ | 1, 5 | 0, 4 |
| 98 | 100, 96 | 100, 96 | 98, 98 | 95, 99 | ⋯ | 1, 5 | 0, 4 |
| 97 | 99, 95 | 99, 95 | 99, 95 | 97, 97 | ⋯ | 1, 5 | 0, 4 |
| ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋱ | ⋮ | ⋮ |
| 3 | 5, 1 | 5, 1 | 5, 1 | 5, 1 | ⋯ | 3, 3 | 0, 4 |
| 2 | 4, 0 | 4, 0 | 4, 0 | 4, 0 | ⋯ | 4, 0 | 2, 2 |
Denoting by the set of strategies available to both players and by the payoff function of one of them we can write
(Note that the other player receives since the game is quantitatively symmetric).
References
- ↑ Kaushik Basu, "The Traveler's Dilemma: Paradoxes of Rationality in Game Theory"; American Economic Review, Vol. 84, No. 2, pp. 391–395; May 1994.
- ↑ Kaushik Basu,"The Traveler's Dilemma"; Scientific American Magazine, June 2007
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Earlier than you decide whether stainless steel cookware is worth buying, lets first discuss what stainless steel cookware is. Chrome steel is manufactured from an alloy, or a mix of metals. Mostly, basic iron with chromium, nickel or another minor metals. The chromium supplies rust safety and gives your cookware durability. The nickel supplies rust safety as effectively, and adds a elegant look. Most properly made chrome steel cookware has copper or aluminum added to the bottom of the pan or pot. That is performed to increases the ability of the pot or pan to conduct heat.
The perfect stainless-steel cookware is the principle category, but nonetheless it is divided into several subcategories primarily based on the standard and the value range. It can be confusing to choose the best chrome steel cookware out of the classes that may meet your necessities. That is where we took a step ahead to explain you all the data that will be useful for you to understand how to choose one of the best stainless steel cookware. The most effective chrome steel cookware set is manufactured from cheap to expensive and high quality constructed pots and pans.
You can find magnetic chrome steel in the layer on the outside of some quality pieces of stainless steel. This is to make it suitable with induction stovetops, which involve the use of a quickly charging electromagnetic area to warmth cookware. Excessive-quality stainless-steel, like All-Clad , makes use of three layers of steel—the austenite layer of metal on the within, ferrite steel on the skin, and a layer of aluminum sandwiched between the 2 for optimum warmth conductivity (metal alone does not conduct heat evenly). Lesser-quality stainless steel is usually just one layer of austenitic chrome steel.
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Arduous-anodized aluminum cookware is likely one of the hottest varieties of materials, despite the fact that many people don't quite perceive the construction. Onerous-anodized aluminum is plain aluminum that has been processed in a collection of chemical baths charged with an electric present. The result's a fabric that has the same superior heat conductivity as aluminum but is non-reactive with acidic foods, such as tomatoes, and twice as exhausting as stainless-steel. Two drawbacks to laborious-anodized cookware are that it is not dishwasher-protected and, because it is not magnetic, it is not going to work with induction vary tops.
The enamel over steel technique creates a bit that has the warmth distribution of carbon steel and a non-reactive, low-stick floor. Such pots are much lighter than most different pots of similar measurement, are cheaper to make than stainless-steel pots, and don't have the rust and reactivity problems with cast iron or carbon steel. citation wanted Enamel over metal is ideal for big stockpots and for other giant pans used largely for water-based cooking. Because of its mild weight and simple cleanup, enamel over metal is also common for cookware used while camping. For more about stainless steel cookware reviews look at our web site. Clad aluminium or copper edit
Distinctive specialty cookware pieces served a la carte to go with any cookware set are constructed of a sturdy Stainless Steel with a brushed exterior end. Designed with an impact bonded, aluminum disk encapsulated base which distributes warmth quickly and evenly to allow precise temperature control. Handles are riveted for durability and performance. The New Specialty Cookware is compatible for all range sorts including induction. Along with the multi use operate, another distinctive characteristic is bottom to prime interior volume markings in both quarts and metric measurement; and every bit comes with a tempered glass lid, oven safe to 350°F.
Whether or not you're a cooking enthusiasts, knowledgeable chef or just cooking for your family you already know the importance of having a totally stocked kitchen. Not solely do you need the appropriate substances, however you additionally need the proper tools to get the job done. In any sort of fundamental cooking training lesson, you will learn that stainless steel is your new greatest friend with regards to kitchen cookware. What you will also study is that high quality cooking tools does not often come at a discounted price. Because of this, it is very important take good care of your cookware! Listed below are some fundamentals for chrome steel care.
To fight the uneven heating downside, most stainless steel pans are laminations of aluminum or copper on the underside to spread the heat around, and stainless steel inside the pan to provide a cooking floor that is impervious to no matter you would possibly put inside. In my expertise, this stainless-steel floor continues to be too sticky to fry on, and should you ever burn it you get a everlasting bother spot. However, sometimes a stainless steel cooking floor turns out to be useful when you can't use aluminum (see under) so I maintain some around. Choose one thing with a fairly thick aluminum layer on the underside.
Effectively, until you’re a metals professional and go inspect the factory where the steel is made to see whether or not their manufacturing process creates a pure austenite with out corrosive materials fashioned, you’re not going to know for certain whether or not the craftsmanship of your stainless is of the best quality. I believe your finest guess is to easily purchase excessive-quality stainless-steel from the beginning, from a brand with a status for good quality. But, I think I have discovered one way which you could determine if the stainless cookware you have already got is doubtlessly reactive.