The Traveler's Dilemma and the Challenge to the Notion of Rationality in Game Theory

MORO, RODRIGO; AUDAY, MARCELO

Buenos Aires

Workshop; Logic Workshop in Buenos Aires: A Tribute to Horacio Arló-Costa; 2012

Sociedad Argentina de Análisis Filosófico (SADAF)

In his paper of 1994, Kaushik Basu presents the Traveler?s Dilemma (TD, henceforth) to challenge the notion of rationality presupposed in Game Theory. On the one hand, this game has only one Nash equilibrium which is also the only rationalizable equilibrium, namely the pair of strategies in the lowest end (i.e., {2,2} in the previous version). To see this point, notice that the strategy 100 is weakly dominated by 99. If 100 is eliminated, 99 is weakly dominated by 98, and so on up to 2 (the only strategy that is not dominated at all). On the other hand, Basu (2007) contends that even for a rational person completely focused on his or her personal profit, it just makes sense to forget about Game Theory and play a high number, expecting that the other person will do so as well. In fact, most people (even experts in Game Theory!) tend to play above the Nash equilibrium in the TD, making on average much more money than the minimal value (see Rubinstein, 2007 for the most extensive study and Becker et al., 2005 for the study with Game Theory experts). Thus, Basu argues that Game Theory does not adequately capture our intuitions about rational decision making. Thus, there are three related questions that demand a response: 1) Which element or elements from Game Theory are responsible for leading to the problematic solution of the TD? 2) How to change Game Theory in such a way that does not longer produce the problematic solution? 3) How to account for people?s behavior at playing the TD? The first goal of this paper is to review literature on this matter, covering both the theoretical side (Basu, 1994, 2007, Brandenburger 2007, Gintis 2009, 2012, Sarangi, 2000) and the empirical side (Becker et al., 2005, Capra et al., 1999, Basu et al., 2011). However, we will focus on the first key question, that is, what exactly is wrong with Game Theory. There is a general agreement in the literature that the key element responsible for the problematic solution in the TD is the assumption of Common Knowledge of Rationality (CKR). We argue that the main problem rather lays in that the proposed solution (2,2) is pareto-dominated. We present three different tentative ways to incorporate this in idea in Game Theory.