Respect for public preferences and iterated backward inference

Abstract
An important approach to game theory is to examine the consequences of beliefs that rational agents may have about each other. This paper considers 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 considers the choice of a “infinitely more likely” than the choice of B; equivalently, 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 [4] and Asheim [1], I treat respect for public preferences as a constraint on lexicographic probability systems. The main result is that if respect for public preferences and perfect recall obtains, then 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.
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