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Limited Computational Resources Favor Rationality

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  • Yuval Salant

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    Abstract

    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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    File URL: http://ratio.huji.ac.il/sites/default/files/publications/dp320.pdf
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    Bibliographic Info

    Paper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp320.

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    Length: 32 pages
    Date of creation: Jul 2003
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    Handle: RePEc:huj:dispap:dp320

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    1. Martin J Osborne & Ariel Rubinstein, 2009. "A Course in Game Theory," Levine's Bibliography 814577000000000225, UCLA Department of Economics.
    2. Michele Piccione & Ariel Rubinstein, 2002. "Modelling the Economic Interaction of Agents with Diverse Abilities to Recognise Equilibrium Patterns," STICERD - Theoretical Economics Paper Series 440, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
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    Cited by:
    1. Jose Apesteguia & Miguel A Ballester, 2007. "On The Complexity of Rationalizing Behavior," Working Papers 320, Barcelona Graduate School of Economics.
    2. Apesteguia, Jose & Ballester, Miguel A., 2010. "The Computational Complexity of Rationalizing Behavior," Journal of Mathematical Economics, Elsevier, vol. 46(3), pages 356-363, May.

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