Abstract
This paper derives a no-trade theorem under Knightian uncertainty, which generalizes the theorem of Milgrom and Stokey (1982, Journal of Economic Theory 26, 17) by allowing general preference relations. It is shown that the no-trade theorem holds true as long as agents' preferences are dynamically consistent in the sense of Machina and Schmeidler (1991, Econometrica 60, 745), and satisfies the so-called piece-wise monotonicity axiom. A preference satisfying the piece-wise monotonicity axiom does not necessarily imply the additive utility representation, nor is necessarily based on beliefs.
Similar content being viewed by others
REFERENCES
Aumann R. (1976), Agreeing to disagree, Annals of Statistics 4, 1236-1239.
Dow J., Madrigal, V. and da Costa Werlang, S.R. (1990), Preferences, common knowledge, and speculative trade, Working paper, Fundaçao Getulio Vargas, Rio de Janeiro.
Ellsberg D. (1961), Risk, ambiguity, and the savage axioms, Quarterly Journal of Economics 75 643-669.
Epstein L. and Le Breton, M. (1993), Dynamically consistent beliefs must be Bayesian, Journal of Economic Theory 61, 1-22.
Geanakoplos, J. (1994), Common knowledge, In: R. Aumann and S. Hart (eds.), Handbook of Game Theory, Volume 2. Elsevier Science, Amsterdam.
Ghirardato P. (1994), Copying with ignorance: Unforeseen contingencies and non-additive uncertainty, UC at Berkeley, mimeo.
Gilboa I. and Schmeidler, D. (1989), Maximin expected utility with non-unique prior, Journal of Mathematical Economics, 18, 141-153.
Holstrom B. and Myerson, R. (1983), Efficient and durable decision rules with incomplete information, Econometrica 51, 1799-1819.
Machina M. and Schmeidler, D. (1992), A more robust definition of subjective probability, Econometrica 60, 745-780.
Milgrom P. and Stokey, N. (1982), Information, trade and common knowledge, Journal of Economic Theory 26, 17-27.
Rubinstein A. and Wolinsky, A. (1990), On the Logic of 'agreeing on disagree' type results, Journal of Economic Theory 51, 184-193.
Savage L.J. (1954), The Foundations of Statistics. New York: Wiley.
Schmeidler D. (1989), Subjective probability and expected utility without additivity, Econometrica 57, 571-587.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ma, C. A No-Trade Theorem under Knightian Uncertainty with General Preferences. Theory and Decision 51, 173–181 (2001). https://doi.org/10.1023/A:1015550925961
Issue Date:
DOI: https://doi.org/10.1023/A:1015550925961