Hellman, Ziv (2007): Common Knowledge and Disparate Priors: When it is O.K. to Agree to Disagree.
Download (835kB) | Preview
Abandoning the oft-presumed common prior assumption, partitioned type spaces with disparate priors are studied. It is shown that in the two-player case, a unique fundamental pair of priors can be identified in each type space, from whose properties boundaries on the possible ranges of expected values under common knowledge can be derived. In the limit as the elements of this pair approach each other,a common prior is identified, and standard results stemming from the common prior assumption are recapitulated. It is further shown that this two-player fundamental pair of priors is a special case of the n-player situation, where a representative n-tuple of fundamentally associated priors can be selected, out of at most n-1 such n-tuples, to play an analogous role.
|Item Type:||MPRA Paper|
|Original Title:||Common Knowledge and Disparate Priors: When it is O.K. to Agree to Disagree|
|Keywords:||common knowledge; heterogeneous prior beliefs; common prior assumption|
|Subjects:||D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D84 - Expectations; Speculations
C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C70 - General
D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D82 - Asymmetric and Private Information; Mechanism Design
|Depositing User:||Ziv Hellman|
|Date Deposited:||06. Jun 2007|
|Last Modified:||12. Feb 2013 11:37|
Aumann, R. Agreeing to Disagree, Annals of Statistics 4 (1976), 1236 -1239
Aumann, R. Correlated Equilibrium as an Expression of Bayesian Rationality, Econometrica 55 (1987), 1-18
Aumann, R. Common Priors: A Reply to Gul, Econometrica 66 (4) (1998), 929-938
Bernheim, B. Axiomatic Characterizations of Rational Choice in Strategic Environments, Scand. J. of Economics 88 (3) (1986) 473-488
Feinberg, Y. Characterizing Common Priors in the Form of Posteriors, Journal of Economic Theory 91 (2) (2000), 127-179
Gale, D. The Theory of Linear Economic Models, New York, McGraw-Hill, 1960.
Geanakoplos, J. and Polemarchakis, H. We Can’t Disagree Forever, Journal of Economic Theory 28 (1) (1982), 192-200
Guillemin, V. and Pollack, A. Differential Topology, Prentice-Hall, New Jersey, 1974.
Gul, F. A Comment on Aumann’s Bayesian View, Econometrica 66 (4) (1998), 923 -927.
Milgrom, P. and Stokey, N., Information, Trade and Common Knowledge, Journal of Economic Theory, 26 (1982), 17 – 27
Monderer, D. and Samet, D. (1989). Approximating Common Knowledge with Common Belief, Games and Economic Behavior 1, 170-190
Morris, S. Trade with Heterogeneous Prior Beliefs and Asymmetric Information, Econometrica, 62 (1995), 1327-1347
Nau, R. The Incoherence of Agreeing to Disagree. Theory and Decision 39 (1995) 219-239
Nehring, K. Common Priors under Incomplete Information: A Unification, Economic Theory, 18 (2001), 535-553
Samet, D. Iterated Expectations and Common Priors, Games and Economic Behavior, 24 (1998), 131-141
Samet, D. Common Priors and Separation of Convex Sets, Games and Economic Behavior, 24 (1998), 172-173
Sebenius, J., and Geanakoplos, J. Don’t bet on it: Contingent agreements with asymmetric information, Journal of the American Statistical Association 78 (1983), 424–426.
Stewart, W. Introduction to the Numerical Solutions of Markov Chains, 1994, Princeton University Press, Princeton, New Jersey