Solution of Traveler’s Dilemma
DOI:
https://doi.org/10.29015/cerem.502Keywords:
game theory, Traveler's dilemma, perfectly rational player, backward inductionAbstract
Aim: The aim of the article is to show: 1) that the reasoning of perfectly rational players presented in 1994 by the author of the Traveler's Dilemma Kaushik Basu is incorrect and therefore leads to wrong conclusions, 2) how the reasoning of these players should look like and what solution it leads to.
Design / Research methods: Logical analysis.
Conclusions / findings: Perfectly rational Traveler’s Dilemma players should use, according to game theory, so-called retrograde (iterative) induction. This is wrong, as in the set of Traveler’s Dilemma games results the principle of transitivity is not met. We believe that perfectly rational players will achieve a better result when they make a random decision from a suitably limited set of decisions. After applying this method of decision making, perfectly rational players will achieve a result similar to those obtained by real players in experiments. Thus, the paradox described in the theory of games disappears, that perfectly rational players achieve worse results than real players
Originality / value of the article: A new way of making decisions in the Traveler’s Dilemma game.
Implications of the research: A new way of making decisions in other games similar to the Traveler’s Dilemma may allow to find new solutions in these games.
Limitations of the research: The described decision-making method can potentially be used in decision-making situations when the following five conditions are met: 1) the set of possible decisions of each player is greater than 2, 2) the winning matrix is known to both players and both know the purpose of their choices, 3) when it is played once with an unknown opponent, 4) when both players have to make their decision without knowing the opponent's choice, 5) when there is no decision, which is a stable balance point or when it is, but its choice means that the player does not achieve a satisfying result.
References
Basu K. On the Nonexistence of Rationality Definition for Extensive Games. International Journal of Game Theory” 1990, vol 19. 33-44
Basu K. The Traveler Dilemma: Paradoxes of Rationality In Game Theory. “American Economic Review”. 1994, 84(2), 391-395.
Basu K. Dylemat podróżnika. “Świat Nauki” (polish edytion “Scientific American”) VII 2007, 7(191). 72-77.
Becker T.,Carter M., Naeve J. Experts Playing the Traveler’s Dilemma. Working Paper 2005, nr 252, Institute for Economics, Hohenheim Uniwersity. ftp://ftp.repec.org/opt/ReDIF/RePEc/hoh/papers/252.pdf
Capra M., Goeree J., Gomez R., and Holt C.. Anomalous Behavior in a Traveler’s Dilemma? “American Economic Review” 1999 89(3), 678-690.
Rubinstein A. „Instinctive and Cognitive Reasoning : A Study of Response Times.” http://www.arielrubinstein.tau.ac.il/papers/Response.pdf
Wolpert, D, Jamison J., Newth D., Harre M. Strategic Choice of Preferences: The Persona Model. “Santa Fe Institute Working Paper” 2011. http://www.santafe.edu/media/workingpapers/11-08-030.pdf
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