## DEFINITION of 'Paradox of Rationality'

The irony that rational decision-making in game theory situations often has poorer payoffs or outcomes than choices made illogically or naively. The paradox of rationality underscores the contradiction between intuition and reasoning according to game theory. This paradox arises because the rational outcomes predicted by backward induction, the main form of game theory analysis, diverge widely from intuitive choices. The paradox of rationality is consistently observed in experimental studies of game theory using such well-known games as prisoner’s dilemma and the centipede game.

## BREAKING DOWN 'Paradox of Rationality'

The paradox of rationality is highlighted by a popular game theory scenario known as the Traveler’s Dilemma, devised by economist Kaushik Basu in 1994. Traveler’s Dilemma presents a scenario in which an airline damages identical antiques purchased by two independent travelers.

When pressed for compensation by the travelers for the damage, the airline manager – who has no clue about the value of the damaged goods – comes up with a novel solution to the problem of estimating the antiques’ value. He tells the two travelers to separately write down the value as any number between $2 and $100. If both write down the same number, the inference is that they are telling the truth and the airline will reimburse them that amount. But if they write different numbers, the manager will assume that the lower number is the actual value and that the higher value is inaccurate. The airline will therefore pay both travelers the lower figure, with a bonus of $2 for the traveler who wrote the lower number and a penalty of $2 for the traveler with the higher number. Thus, if A writes $50 and B write $55, A receives $52 ($50 + $2 bonus) as compensation, while B gets $48 ($50 - $2 penalty).

According to backward induction, the rational choice in terms of the Nash equilibrium is $2. However, in experimental studies, most people pick $100 or a number close to it. This includes people who have made a naïve selection without thinking the problem through, as well as those who are aware that they are deviating from the rational choice. The fact that substantially higher payoffs are possible by rejecting the rational choice and acting illogically or naively is the paradox of rationality.