Conclusion
In this paper we analyzed the Traveler's Dilemma. While analyzing the dilemma using classical game theory, we found the rationalizable Nash equilibrium in which both players choose the number 2. However, human players do not make this choice very often in practice, and even simulations done by computers seem to indicate otherwise.Changing the reward for being honest (or for just being lucky to have chosen the lowest number) to a number higher than 2 should theoretically have no impact on the strategy a player will use, but in practice it turns out that it actually does have impact on the choices human players make. When the reward is high enough, people tend to choose their number closer and closer to the Nash equilibrium.
From these facts we can conclude that classical game theory does not give an accurate description on how this game is played or should be played to maximize profit. When looking at how humans play the game, it appears that humans tend to assume some degree of cooperation from the other player. Human players realize that cooperating will increase the payout of both players, so a player benefits from choosing a high number, assuming the other player chooses a high number as well. Even game theory experts, who should know about the Nash equilibrium and the theoretical problems in this dilemma, tend to assume a degree of cooperation from the other player.
In short, the 'optimal' strategy provided by classical game theory does not give a satisfying or realistic results, but looking at computer simulations or at humans playing the game can provide better explanations on how the game is played, or should be played, in practice.