The Nash Equilibrium and the traveller's dilemma

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The confusion appears to be that the dilemma assumes (while stating it does not) that the travellers are playing against each other where in the story they are not playing a game but just both trying to get as much money as possible.

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The solution simply assumes that each player tries to make the most money possible.

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This is the truth, but not quite the "whole truth." The whole truth would add that each player KNOWS that their opponent is perfectly rational, is seeking the same goal, and that their opponent knows this of them. Then the solution follows.

The marginal utility of a guaranteed 2$ pales in comparison to the marginal utility of a possible 100$. This is why "normal" people would choose 100, and why they would expect other normal people to do so. A rational agent can "beat" this by playing 99, but has gained only 1$ relative to the "stable" strategy of both players playing 100$. In real life, we make these decisions as if we plan to play the game over and over, and a player who consistently played 99, in an effort to get this tiny edge, would most likely not get invited to play this positive sum game very often.

Hence we see how it relates to poker: the "reasonable" choice is the one that keeps the game going and is profitable for everybody. The "rational" choice is one that is unexploitable, but it also ensures no one will want to play against you.