Abstract
An example is given in which agents agree to disagree in a countable space of equiprobable states of nature. Even in this unorthodox setting, if the sets of the information partitions are intervals, an agreement theorem holds. A result that describes the margin for disagreement is also obtained.
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References
Aumann R.J.: Agreeing to disagree. Ann Stat 4, 1236–1239 (1976)
Chang J.T., Pollard D.: Conditioning as disintegration. Stat Neerl 51(3), 287–317 (1997)
de Finetti B.: Theory of Probability, vols. 1 and 2. Wiley, New York (1974)
Feinberg Y.: Characterizing common priors in the form of posteriors. J Econ Theory 91, 127–179 (2000)
Geanakoplos J.: Common knowledge. In: Aumann, R.J., Hart, S. (eds) Handbook of Game Theory with Economic Applications, vol. II chap. 40, pp. 1437–1496. Elsevier, Amsterdam (1994)
Geanakoplos J., Polemarchakis H.: We can’t disagree forever. J Econ Theory 28, 192–200 (1982)
Harsanyi, J.C.: Games with incomplete information played by Bayesian players, Parts I–III. Manage Sci 14, 159–182, 320–334, 486–502 (1967–68)
Heifetz A.: The positive foundation of the common prior assumption. Games Econ Behav 56(1), 105–120 (2006)
Morris S.: The common prior assumption in economic theory. Econ Phil 11, 227–253 (1995)
Samet D.: Agreeing to disagree in infinite information structures. Int J Game Theory 21, 213–218 (1992)
Samet D.: Common priors and the separation of convex sets. Games Econ Behav 24, 172–174 (1998)
Savage L.J.: The Foundations of Statistics. Wiley, New York (1954)
Stinchcombe M.: Countably additive subjective probabilities. Rev Econ Stud 64, 125–146 (1997)
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I am grateful to Carlos Hervés Beloso, Ali Khan, David Levine, Juan Pablo Torres-Martínez, Nicholas Yannelis (Editor) and an anonymous referee for helpful suggestions and encouragement, and thank participants in the Conference in Honor of Prof. Wayne Shafer, held at the University of Illinois at Urbana-Champaign, and in the XVII European GE Workshop in Paestum. Financial support from CEMPRE and research grant PTDC/ECO/66186/2006 from Fundação para a Ciência e Tecnologia and FEDER is acknowledged.
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Correia-da-Silva, J. Agreeing to disagree in a countable space of equiprobable states of nature. Econ Theory 45, 291–302 (2010). https://doi.org/10.1007/s00199-009-0439-z
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DOI: https://doi.org/10.1007/s00199-009-0439-z
Keywords
- Agreeing to disagree
- Interactive epistemology
- Theory of probability
- Countable additivity
- Bounded rationality