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Second-Order Induction: Uniqueness and Complexity

Author

Listed:
  • Rossella Argenziano

    (Department of Economics - University of Essex)

  • Itzhak Gilboa

    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique)

Abstract

Agents make predictions based on similar past cases, while also learning the relative importance of various attributes in judging similarity. We ask whether the resulting "empirical similarity" is unique, and how easy it is to find it. We show that with many observations and few relevant variables, uniqueness holds. By contrast, when there are many variables relative to observations, non-uniqueness is the rule, and finding the best similarity function is computationally hard. The results are interpreted as providing conditions under which rational agents who have access to the same observations are likely to converge on the same predictions, and conditions under which they may entertain different probabilistic beliefs.

Suggested Citation

  • Rossella Argenziano & Itzhak Gilboa, 2018. "Second-Order Induction: Uniqueness and Complexity," Working Papers hal-01933887, HAL.
    • Handle: RePEc:hal:wpaper:hal-01933887
    DOI: 10.2139/ssrn.3178712
    as

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    Keywords

    Empirical Similarity; Belief Formation;

    JEL classification:

    • A10 - General Economics and Teaching - - General Economics - - - General

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