A choice function is a rule that chooses a single alternative from every set of alternatives drawn from a finite ground set. A rationalizable choice function satisfies the consistency condition; i.e., if an alternative is chosen from a set A, then the same alternative is also chosen from every subset of A that contains it. In this paper we study computational aspects of choice, through choice functions. We explore two simple models that demonstrate two important aspects of choice procedures: the ability to remember the past and the ability to perform complex computations. We show that a choice function is optimal in terms of the amount of memory and the computational power required for its computation if and only if the function is rationalizable. We also show that the computation of most other choice functions, including some “natural” ones, requires much more memory and computational power.
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Paper provided by Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem in its series Discussion Paper Series with number
dp320.
References listed on IDEAS Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
Martin J. Osborne & Ariel Rubinstein, 1994.
"A Course in Game Theory,"
MIT Press Books,
The MIT Press,
edition 1, volume 1, number 0262650401.
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