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Limited Computational Resources Favor Rationality

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  • Yuval Salant

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.

Suggested Citation

  • Yuval Salant, 2003. "Limited Computational Resources Favor Rationality," Discussion Paper Series dp320, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    • Handle: RePEc:huj:dispap:dp320
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    References listed on IDEAS

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    1. Michele Piccione & Ariel Rubinstein, 2003. "Modeling the Economic Interaction of Agents With Diverse Abilities to Recognize Equilibrium Patterns," Journal of the European Economic Association, MIT Press, vol. 1(1), pages 212-223, March.
    2. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
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    Cited by:

    1. Dimitrov, Dinko & Mukherjee, Saptarshi & Muto, Nozomu & 無藤, 望, 2013. "List-based decision problems," Discussion Papers 2013-02, Graduate School of Economics, Hitotsubashi University.
    2. Jose Apesteguia & Miguel A. Ballester, 2007. "On the complexity of rationalizing behavior," Economics Working Papers 1048, Department of Economics and Business, Universitat Pompeu Fabra.
    3. Yongjie Yang & Dinko Dimitrov, 2019. "The complexity of shelflisting," Theory and Decision, Springer, vol. 86(1), pages 123-141, February.
    4. Dinko Dimitrov & Saptarshi Mukherjee & Nozomu Muto, 2016. "‘Divide-and-choose’ in list-based decision problems," Theory and Decision, Springer, vol. 81(1), pages 17-31, June.
    5. Brenčič, Vera, 2014. "Search online: Evidence from acquisition of information on online job boards and resume banks," Journal of Economic Psychology, Elsevier, vol. 42(C), pages 112-125.
    6. Apesteguia, Jose & Ballester, Miguel A., 2010. "The Computational Complexity of Rationalizing Behavior," Journal of Mathematical Economics, Elsevier, vol. 46(3), pages 356-363, May.
    7. Guney, Begum, 2014. "A theory of iterative choice in lists," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 26-32.

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