The Rationality of Irrationality for Managers : Returns-Based Beliefs and the Traveler's Dilemma

This paper discusses the importance of paradoxes of irrationality for managers by elaborating upon the rational basis for the adoption of non-equilibrium strategies in game theory. It does so by revisiting the one-shot Traveler's Dilemma game, proposing a solution which reconciles the anomaly between the empirical findings and the theoretical predictions of the Nash equilibrium suggested by the game. We contend that this seeming irrationality may be based upon the subjective probabilities of the players. We proffer an alternative basis upon which beliefs in game theory might be formed - 'returns-based beliefs' - and we present the corresponding numerical results for the Traveler's Dilemma game. The importance of returns-based beliefs forming the subjective probabilities arises also because we show that they can be applied even when the players are not aware of their respective histories. We show that as long as the penalty is not too severe, then players are likely to play a high claim strategy. Our results correspond very closely to other empirical studies of the Traveler's Dilemma. Therefore, we argue that understanding the rational basis for game-theoretic paradoxes of irrationality might have important and practical uses for managerial decision-making