On the nonexistence of universal information structures

This paper extends the nonexistence result of Heifetz and Samet (Games Econ. Behav. 22 (1998) 260 273). They have shown that there exists no universal knowledge space to which every knowledge space can be mapped in a knowledge-preserving manner. We show that an analogous nonexistence result holds in the more general context of information structures. These structures can be viewed as generalizations of knowledge spaces that describe non-probabilistic beliefs. (c) 2003 Elsevier Inc. All rights reserved.

[1]  Dov Samet,et al.  Knowledge Spaces with Arbitrarily High Rank , 1998 .

[2]  D. Samet.  Ignoring ignorance and agreeing to disagree , 1990 .

[3]  Microeconomics-Charles W. Upton.  Repeated games , 2020, Game Theory.

[4]  Robert J. Aumann,et al.  Interactive epistemology II: Probability , 1999, Int. J. Game Theory.

[5]  Polly S Nichols,et al.  Agreeing to disagree. , 2005, General dentistry.

[6]  David M. Kreps,et al.  Rationality and knowledge in game theory , 1997 .

[7]  J. Geanakoplos.  Game Theory Without Partitions, and Applications to Speculation and Consensus , 1989, The B.E. Journal of Theoretical Economics.

[8]  Eddie Dekel,et al.  Hierarchies of Beliefs and Common Knowledge , 1993 .

[9]  Ariel Rubinstein,et al.  A Comment on the Logic of 'Agreeing to Disagree' Type Results , 1988 .

[10]  A. Heifetz.  The bayesian formulation of incomplete information — The non-compact case , 1993 .

[11]  A. Rubinstein.  Modeling Bounded Rationality , 1998 .

[12]  Ronald Fagin,et al.  Reasoning about knowledge , 1995 .

[13]  David M. Kreps,et al.  Advances In Economics and Econometrics: Theory And Applications: Seventh World Congress , 1997 .

[14]  S. Zamir,et al.  Formulation of Bayesian analysis for games with incomplete information , 1985 .

[15]  J. Geanakoplos,et al.  Correlated equilibrium with generalized information structures , 1992 .

[16]  Robert J. Aumann,et al.  Interactive epistemology I: Knowledge , 1999, Int. J. Game Theory.

[17]  Aviad Heifetz.  Infinitary S5-Epistemic Logic , 1997, Math. Log. Q..

[18]  J. Harsanyi.  Games with Incomplete Information Played by 'Bayesian' Players, Part III. The Basic Probability Distribution of the Game , 1968 .

[19]  Saul A. Kripke,et al.  Semantical Analysis of Modal Logic I Normal Modal Propositional Calculi , 1963 .

[20]  A. Heifetz,et al.  Topology-Free Typology of Beliefs , 1998 .

[21]  Sylvain Sorin,et al.  Repeated Games. Part A: Background Material , 1994 .