Quantified beliefs and believed quantities. (English) Zbl 0967.91079
Author’s summary: Beliefs about quantities are expressed by estimations. Beliefs are quantified by ascribing to them probability numbers. It is, shown that beliefs about quantities and quantified beliefs give rise to the same model, that of a type space. The author studies the axiom that an agent’s estimation coincides with the estimation of that estimation, showing it to be weaker than the introspection axiom, according to which an agent is certain of his own probabilistic beliefs. It implies, however, that the agent is certain that he is introspective, and it is equivalent to the axioms of averaging and conditioning, which are expressed in terms of probabilistic beliefs.
MSC:
| 91C05 | Measurement theory in the social and behavioral sciences |
| 60A99 | Foundations of probability theory |
| 91B02 | Fundamental topics (basic mathematics, methodology; applicable to economics in general) |
References:
| [1] | Aumann, R. J., Interactive epistemology II: probability, Int. J. Game Theory, 28, 301-314 (1999) · Zbl 0961.91039 |
| [2] | Fagin, R.; Halpern, J. Y.; Megiddo, N., A logic of reasoning about probabilities, Info. Comput., 87, 78-128 (1990) · Zbl 0811.03014 |
| [3] | Gaifman, H., A theory of higher order probabilities, (Skyrms, B.; Harper, W., Causation, Chance and Credence (1988), Kluwer Academic: Kluwer Academic Dordrecht/Norwell) · Zbl 0192.03302 |
| [4] | Harsanyi, J. C., Games with incomplete information played by Bayesian players, parts I, II, & III, Man. Sc., 14, 159-182 (1967-68) · Zbl 0207.51102 |
| [5] | Halpern, J. Y., The relationship between knowledge, belief and certainty, Ann. Math. Artificial Intelligence, 4, 301-322 (1991) · Zbl 0865.03016 |
| [6] | Halpern, J. Y., Errata: The relationship between knowledge, belief and certainty, Ann. Math. Artificial Intelligence, 26, 253-256 (1999) · Zbl 0865.03016 |
| [7] | A. Heifetz, and, P. Mongin, Probability logic for type spaces, Games Econ. Behavior, forthcoming.; A. Heifetz, and, P. Mongin, Probability logic for type spaces, Games Econ. Behavior, forthcoming. · Zbl 0978.03017 |
| [8] | A. Heifetz, and, D. Samet, Topology-free typology of beliefs, J. Econ. Theory, forthcoming.; A. Heifetz, and, D. Samet, Topology-free typology of beliefs, J. Econ. Theory, forthcoming. · Zbl 0921.90156 |
| [9] | Jeffrey, R., Probability and the Art of Judgment (1992), Cambridge University Press: Cambridge University Press Cambridge |
| [10] | Krengel, U., Ergodic Theorems. Ergodic Theorems, Studies in Math., 6 (1985), de Gruyter: de Gruyter Berlin · Zbl 0471.28011 |
| [11] | Mertens, J. F.; Zamir, S., Formulation of Bayesian analysis for games with incomplete information, Int. J. Game Theory, 14, 1-29 (1985) · Zbl 0567.90103 |
| [12] | Samet, D., Iterative expectations and common priors, Games Econ. Behavior, 24, 131-141 (1997) · Zbl 0910.90285 |
| [13] | Monderer, D.; Samet, D., Approximating common knowledge with common beliefs, Games Econ. Behavior, 1, 170-190 (1989) · Zbl 0755.90110 |
| [14] | Skyrms, B., Causal Necessity (1980), Yale University Press: Yale University Press New Haven |
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