- Traveler's dilemma
In

game theory , the**traveler's dilemma**(sometimes abbreviated**TD**) is a type of non-zero-sum game in which two players attempt to maximise 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: [] [Kaushik Basu , "The Traveler's Dilemma: Paradoxes of Rationality in Game Theory"; "American Economic Review", Vol. 84, No. 2, pages 391-395; May 1994.*Kaushik Basu, [*] :*http://www.sciam.com/article.cfm?chanID=sa006&colID=1&articleID=7750A576-E7F2-99DF-3824E0B1C2540D47 "The Traveler's Dilemma"*] ; "Scientific American Magazine", June 2007"An airline loses two suitcases belonging to two different travelers. Both suitcases happen to be identical and contain identical antiques. An airline manager tasked to settle the claims of both travelers explains that the airline is liable for a maximum of $100 per suitcase, 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 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 (often abbreviated "PD") and thus TD can be viewed as an extension of PD. The traveler's dilemma is also related to the gameGuess 2/3 of the average in that both involve deep iterative deletion of dominated strategies in order to demonstrate theNash equilibrium , and that both lead to experimental results that deviate markedly from the game-theoretical predictions.For the traveler's dilemma,

game theory predicts that both will write down the value '$2' if their strategies were purely rational. The $2 in this instance is theNash equilibrium point for the game. However, when the game is played experimentally, most participants select the value '$100' or a value close to '$100', including those who have not thought through the logic of the decision as well as those who understand themselves to be making a non-rational choice. Furthermore, the travelers are rewarded by deviating strongly from theNash equilibrium in the game and obtain much higher rewards than would be realized with the purely rational strategy. These experiments fail to show either that most people use purely rational strategies nor that they would be better off financially if they were to do so. The paradox has led some to question the value of game theory in general, whilst 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.**Payoff matrix**The canonical

payoff matrix is shown below (if only integer inputs are taken into account):**References**

*Wikimedia Foundation.
2010.*

### Look at other dictionaries:

**Prisoner's dilemma**— This article is about game theory. For the 1988 novel, see Prisoner s Dilemma (novel). For the Doctor Who audiobook, see The Prisoner s Dilemma. For the 2001 play, see The Prisoner s Dilemma (play). The prisoner’s dilemma is a canonical example… … Wikipedia**Unscrupulous diner's dilemma**— In game theory, the Unscrupulous diner s dilemma (or just Diner s dilemma) is an n player prisoner s dilemma. The situation imagined is that several individuals go out to eat, and prior to ordering they agree to split the check equally between… … Wikipedia**Nash equilibrium**— A solution concept in game theory Relationships Subset of Rationalizability, Epsilon equilibrium, Correlated equilibrium Superset of Evolutionarily stable strategy … Wikipedia**Tragedy of the commons**— Cows on Selsley Common. The tragedy of the commons is one way of accounting for overexploitation. The tragedy of the commons is a dilemma arising from the situation in which multiple individuals, acting independently and rationally consulting… … Wikipedia**n-player game**— In game theory, an n player game is a game which is well defined for any number of players. This is usually used in contrast to standard 2 player games that are only specified for two players. In defining n player games, game theorists usually… … Wikipedia**Chicken (game)**— For other uses, see Chicken (disambiguation). The game of chicken, also known as the hawk dove or snowdrift[1] game, is an influential model of conflict for two players in game theory. The principle of the game is that while each player prefers… … Wikipedia**No-win situation**— A no win situation, also called a lose lose situation, is one where a person has choices, but no choice leads to a net gain. For example, if an executioner offers the condemned the choice of dying by being hanged, shot, or poisoned, since all… … Wikipedia**Normal-form game**— In game theory, normal form is a way of describing a game. Unlike extensive form, normal form representations are not graphical per se, but rather represent the game by way of a matrix. While this approach can be of greater use in identifying… … Wikipedia**Deadlock (game theory)**— C D c 1, 1 0, 3 d 3, 0 2, 2 In game theory, Deadlock is a game where the action that is mutually most beneficial is also dominant. (An example payoff matrix for Deadlock is pictured to the right.) This provides a contrast to the Prisoner s… … Wikipedia**Best response**— In game theory, the best response is the strategy (or strategies) which produces the most favorable outcome for a player, taking other players strategies as given (Fudenberg Tirole 1991, p. 29; Gibbons 1992, pp. 33–49). The concept of a … Wikipedia