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Games with Incomplete Information Played by "Bayesian" Players Part II. Bayesian Equilibrium Points

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  • John C. Harsanyi

    (Univeristy of California, Berkeley)

Abstract

Part I of this paper has described a new theory for the analysis of games with incomplete information. It has been shown that, if the various players' subjective probability distributions satisfy a certain mutual-consistency requirement, then any given game with incomplete information will be equivalent to a certain game with complete information, called the "Bayes-equivalent" of the original game, or briefly a "Bayesian game." Part II of the paper will now show that any Nash equilibrium point of this Bayesian game yields a "Bayesian equilibrium point" for the original game and conversely. This result will then be illustrated by numerical examples, representing two-person zero-sum games with incomplete information. We shall also show how our theory enables us to analyze the problem of exploiting the opponent's erroneous beliefs. However, apart from its indubitable usefulness in locating Bayesian equilibrium points, we shall show it on a numerical example (the Bayes-equivalent of a two-person cooperative game) that the normal form of a Bayesian game is in many cases a highly unsatisfactory representation of the game situation and has to be replaced by other representations (e.g., by the semi-normal form). We shall argue that this rather unexpected result is due to the fact that Bayesian games must be interpreted as games with "delayed commitment" whereas the normal-form representation always envisages a game with "immediate commitment."

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File URL: http://dx.doi.org/10.1287/mnsc.14.5.320
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Bibliographic Info

Article provided by INFORMS in its journal Management Science.

Volume (Year): 14 (1968)
Issue (Month): 5 (January)
Pages: 320-334

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Handle: RePEc:inm:ormnsc:v:14:y:1968:i:5:p:320-334

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Cited by:
  1. repec:pdn:wpaper:64 is not listed on IDEAS
  2. FIGUIERES, Charles & TIDBALL, Mabel & JEAN-MARIE, Alain, 2001. "On the effects of conjectures in a symmetric strategic setting," CORE Discussion Papers 2001038, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Sonja Brangewitz & Claus-Jochen Haake, 2013. "Cooperative Transfer Price Negotiations under Incomplete Information," Working Papers CIE 64, University of Paderborn, CIE Center for International Economics.
  4. Garrouste, Christelle & Loi, Massimo, 2009. "Applications De La Theorie Des Jeux A L'Education: Pour Quels Types Et Niveaux D'Education, Quels Modeles, Quels Resultats?
    [Applications of Game Theory in Education - What Types and At What Levels
    ," MPRA Paper 31825, University Library of Munich, Germany.
  5. Zonderland, Maartje E. & Timmer, Judith, 2012. "Optimal allocation of MRI scan capacity among competing hospital departments," European Journal of Operational Research, Elsevier, vol. 219(3), pages 630-637.

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