Iterated backward inference: an algorithm for proper rationalizability

Oliver Schulte

Abstract: An important approach to game theory is to examine the consequences of beliefs that agents may have about each other. This paper investigates respect for public preferences. Consider an agent A who believes that B strictly prefers an option a to an option b. Then A respects B's preference if A assigns probability 1 to the choice of a given that B chooses a or b. Respect for public preferences requires that if it is common belief that B prefers a to b, then it is common belief that all other agents respect that preference. Along the lines of Blume, Brandenburger and Dekel [3] and Asheim [1], I treat respect for public preferences as a constraint on lexicographic probability systems. The main result is that given respect for public preferences and perfect recall, players choose in accordance with Iterated Backward Inference. Iterated Backward Inference is a procedure that generalizes standard backward induction reasoning for games of both perfect and imperfect information. From Asheim's characterization of proper rationalizability [1] it follows that properly rationalizable strategies are consistent with respect for public preferences; hence strategies eliminated by Iterated Backward Inference are not properly rationalizable.