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Interactive epistemology I: Knowledge

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Author Info
Robert J. Aumann () (Center for Rationality and Interactive Decision Theory, The Hebrew University, Feldman Building, Givat Ram, 91904 Jerusalem, Israel)

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Abstract

Formal Interactive Epistemology deals with the logic of knowledge and belief when there is more than one agent or "player." One is interested not only in each person's knowledge about substantive matters, but also in his knowledge about the others' knowledge. This paper examines two parallel approaches to the subject. The first is the semantic approach, in which knowledge is represented by a space of states of the world, together with partitions ℐi of for each player i; the atom of ℐi containing a given state of the world represents i's knowledge at that state - the set of those other states that i cannot distinguish from . The second is the syntactic approach, in which knowledge is embodied in sentences constructed according to certain syntactic rules. This paper examines the relation between the two approaches, and shows that they are in a sense equivalent.

In game theory and economics, the semantic approach has heretofore been most prevalent. A question that often arises in this connection is whether, in what sense, and why the space and the partitions ℐi can be taken as given and commonly known by the players. An answer to this question is provided by the syntactic approach.

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Publisher Info
Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 28 (1999)
Issue (Month): 3 ()
Pages: 263-300
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Handle: RePEc:spr:jogath:v:28:y:1999:i:3:p:263-300

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Related research
Keywords: Epistemology · interactive epistemology · knowledge · common knowledge · semantic · syntactic · model;

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  1. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2006. "A Canonical Model for Interactive Unawareness," Working Papers 05-7, University of California at Davis, Department of Economics. [Downloadable!]
    Other versions:
  2. Felipe Zurita, 2005. "Beyond Earthquakes: The New Directions of Expected Utility Theory," Cuadernos de Economía (Latin American Journal of Economics), Instituto de Economía. Pontificia Universidad Católica de Chile., vol. 42(126), pages 209-255. [Downloadable!]
    Other versions:
  3. Yi-Chun Chen & Ngo Van Long & Xiao Luo, 2007. "Iterated Strict Dominance in General Games," CIRANO Working Papers 2007s-03, CIRANO. [Downloadable!]
    Other versions:
  4. Robin Cubitt & Robert Sugden, 2005. "Common reasoning in games: a resolution of the paradoxes of ‘common knowledge of rationality’," Discussion Papers 2005-17, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham. [Downloadable!]
  5. Slikker, M. & Norde, H. & Tijs, S., 2000. "Information sharing games," Discussion Paper 100, Tilburg University, Center for Economic Research. [Downloadable!]
  6. Dov Samet, 2008. "The sure-thing principle and independence of irrelevant knowledge," Levine's Bibliography 122247000000002297, UCLA Department of Economics. [Downloadable!]
  7. Dov Samet, 2008. "S5 Knowledge Without Partitions," Levine's Bibliography 122247000000001875, UCLA Department of Economics. [Downloadable!]
  8. Oliver Board, 2002. "Dynamic Interactive Epistemology," Economics Series Working Papers 125, University of Oxford, Department of Economics. [Downloadable!]
    Other versions:
  9. Shmuel Zamir, 2008. "Bayesian games: Games with incomplete information," Discussion Paper Series dp486, Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem. [Downloadable!]
  10. Adam Brandenburger, 2007. "The power of paradox: some recent developments in interactive epistemology," International Journal of Game Theory, Springer, vol. 35(4), pages 465-492, April. [Downloadable!] (restricted)
  11. Branzei, R. & Tijs, S. & Timmer, J., 2000. "Collecting information to improve decision-making," Discussion Paper 26, Tilburg University, Center for Economic Research. [Downloadable!]
  12. MEIER, Martin, 2001. "An infinitary probability logic for type spaces," CORE Discussion Papers 2001061, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
  13. Moscati Ivan, 2009. "Interactive and common knowledge in the state-space model," CESMEP Working Papers 200903, University of Turin. [Downloadable!]
  14. Ehud Lehrer & Dov Samet, 2003. "Agreeing to agree," Game Theory and Information 0310005, EconWPA. [Downloadable!]
  15. Xiao Luo & Yi-Chun Chen, 2004. "A Unified Approach to Information, Knowledge, and Stability," Econometric Society 2004 Far Eastern Meetings 472, Econometric Society. [Downloadable!]
  16. Dov Samet, 2006. "Agreeing to disagree: The non-probabilistic case," Levine's Bibliography 321307000000000536, UCLA Department of Economics. [Downloadable!]
  17. Pier Luigi Porta & Gianni Viaggi, 2002. "Employment, Technology and Institutions in the Process of Structural Change. A History of Economic Thought Perspective," Working Papers 51, University of Milano-Bicocca, Department of Economics, revised Jul 2002. [Downloadable!]
  18. Shmuel Zamir, 2008. "Bayesian games: games of incomplete information," Levine's Bibliography 122247000000002215, UCLA Department of Economics. [Downloadable!]
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