Limited Computational Resources Favor Rationality
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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- Michele Piccione & Ariel Rubinstein, 2010.
"Modeling the Economic Interaction of Agents with Diverse Abilities to Recognize Equilibrium Patterns,"
Levine's Working Paper Archive
506439000000000108, David K. Levine.
- 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, 03.
- 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.
- Michele Piccione & Ariel Rubinstein, 2002. "Modelling the economic interaction of agents with diverse abilities to recognise equilibrium patterns," LSE Research Online Documents on Economics 2061, London School of Economics and Political Science, LSE Library.
- Martin J. Osborne & Ariel Rubinstein, 1994.
"A Course in Game Theory,"
MIT Press Books,
The MIT Press,
edition 1, volume 1, number 0262650401, June.
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