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Definition: Paradox of Rationality
It is a concept of game theory that suggests that players sometimes choose irrational options because they are likely to get them better payoffs. In case of such a paradox, the rational choice of the game (that ought to be picked) is avoided by the player for the sake of enjoying a better reward.
In a game theoretic setup, some games can be solved by backward induction method to arrive at the equilibrium solution. The equilibrium solution is supposed to be the rational choice of action for all players. However, there are cases when players avoid the rational choice arrived at by backward induction.
For example, in a centipede game, there are two players and two piles of coins – one bigger pile and one smaller pile. At start, the first player has the opportunity to either pick the bigger pile, give the second player the smaller pile and finish the game, or pass both piles to the second player and double the coins in both. The second player can do the same – either end the game by picking the bigger pile or pass on both piles and double the coins.
As per backward induction the game has to end in the first round with the first player picking the larger pile. This is because the first player knows that the other player playing the last round will pick the bigger pile and ditch, predicting which he/she would want to defect in the second last round. The same prediction when continued will result in the game ending right in the first move.
However, empirical results have shown that most players tend to continue the game for some time in pursuit of better results as against the rationale choice predicted by backward induction. This is the paradox of rationality. Other classical examples of paradox of rationality are the games of Prisoner’s Dilemma and Traveler’s Dilemma.