Analyzing The Traveler's Dilemma

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• Index
• Introduction
• Game Theory
• Real-life Strategies
• Conclusions
• References
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Introduction

The traveler's dilemma [1,2], is described with the following parable.

Two travelers returning home from a remote island, where they bought identical antiques (or, rather, what the local tribal chief, while choking on suppressed laughter, described as ''antiques''), discover that the airline has managed to smash these, as airlines generally do. The airline manager who is described by his juniors as a ''corporate whiz'', by which they mean a ''man of low cunning,'' assures the passengers of adequate compensation. But since he does not know the cost of the antique, he offers the following scheme.
Each of the two travelers has to write down on a piece of paper the cost of the antique. This can be any value between $2$ units of money and $100$ units. Denote the number chosen by traveler $i$ by $n_i$. If both write the same number, that is, $n_i$ = $n_j$, then it is reasonable to assume that they are telling the truth (so argues the manager) and so each of these travelers will be paid $n_i$ (or $n_j$) units of money.
If traveler $i$ writes a larger number than the other (i.e., $n_i > n_j$), then it is reasonable to assume (so it seems to the manager) that $j$ is being honest and $i$ is lying. In that case the manager will treat the lower number, that is, $n_j$, as the real cost and will pay traveler $i$ the sum of $n_j -2$ and pay $j$ the sum of $n_j +2$. traveler $i$ is paid $2$ units less as penalty for lying and $j$ is paid $2$ units more as reward for being so honest in relation to the other traveler.
Given that each traveler or player wants to maximize his payoff (or compensation) what outcome should one expect to see in the above game? In other words, which pair of strategies, ($n_i$,$n_j$), will be chosen by the players?


In this paper, we will analyze the Traveler's Dilemma from several angles, and try some variations on it, like changing the reward. From these analyses we will try to explain this apparent contradiction between classical game theory and human behaviour.