Refinements and higher-order beliefs: a unified survey

  • Atsushi Kajii
  • Stephen Morris
Special Section: Article Fundamental Issues in Game Theory and Market Design


This paper presents a simple framework that allows us to survey and relate some different strands of the game theory literature. We describe a “canonical” way of adding incomplete information to a complete information game. This framework allows us to give a simple “complete theory” interpretation (Kreps in Game theory and economic modelling. Clarendon Press, Oxford, 1990) of standard normal form refinements such as perfection, and to relate refinements both to the “higher-order beliefs literature” (Rubinstein in Am Econ Rev 79:385–391, 1989; Monderer and Samet in Games Econ Behav 1:170–190, 1989; Morris et al. in Econ J Econ Soc 63:145–157, 1995; Kajii and Morris in Econ J Econ Soc 65:1283–1309, 1997a) and the “payoff uncertainty approach” (Fudenberg et al. in J Econ Theory 44:354–380, 1988; Dekel and Fudenberg in J Econ Theory 52:243–267, 1990).


Higher order beliefs Incomplete information Refinements Robustness 



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Copyright information

© Japanese Economic Association 2020

Authors and Affiliations

  • Atsushi Kajii
    • 1
    • 4
  • Stephen Morris
    • 2
    • 3
    • 5
  1. 1.Institute of Policy and Planning SciencesUniversity of TsukubaTsukubaJapan
  2. 2.Northwestern UniversityChicagoUSA
  3. 3.University of PennsylvaniaPhiladelphiaUSA
  4. 4.Kwansei Gakuin UniversityNishinomiyaJapan
  5. 5.Massachusetts Institute of TechnologyCambridgeUSA

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