Abstract
The theory of games against nature relies on complete preferences among all conceivable acts (case 1). Aumann and Drèze (Am Econ J Microecon 1(1):1–16, 2009) consider situations where preferences are defined only for a given set of acts (case 2). We extend these results to situations where (i) only the set of optimal elements from a given set of acts is known (case 3); (ii) only a single optimal act is known (case 4). To these four cases correspond four nested sets of admissible subjective probabilities. Cases 3 and 4 define the extent to which probabilities must be specified to solve a decision problem.
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References
Anscombe FJ, Aumann RJ (1963) A definition of subjective probability. Ann Math Stat 34: 199–205
Aumann RJ (1962) Utility theory without the completeness axiom. Econometrica 30: 445–462
Aumann RJ, Drèze JH (2009) Assessing strategic risk. Am Econ J Microecon 1(1): 1–16 (ASR in the text)
Castagnoli E, Maccheroni F, Marinacci M (2003) Expected utility with multiple priors. In: Bernard JM, Seidenfeld T, Zaffalon M (eds) Proceedings of the third international symposium on imprecise probabilities and its applications. Carleton Scientific, Waterloo (Canada), pp 121–132
Drèze JH (1987) Decision theory with moral hazard and state-dependent preferences. In: Drèze JH (ed) Essays on economic decisions under uncertaintanty. Cambridge University Press, Cambridge, pp 23–89
Dubra J, Maccheroni F, Ok EA (2004) Expected utility theory without the completeness axiom. J Econ Theory 115: 118–133
Luce RD, Raiffa H (1957) Games and decisions. Wiley, New York
Nemhauser GL, Wolsey LA (1988) Integer and combinatorial optimisation. Wiley, New York
Rockafellar RT (1970) Convex analysis. Princeton University Press, Princeton
Samuelson PA (1938) A note on the pure theory of consumer’s behaviour. Economica NS 5: 61–71
Savage LJ (1954) Foundations of statistics. Wiley, New York
von Neumann J, Morgenstern O (1944) Theory of games and economic behaviour. Princeton University Press, Princeton
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This paper is an outgrowth of joint research with R.J. Aumann (2009), and I regard it as joint work. Because I wrote up the paper on my own (after some e-mail exchanges), Aumann tactfully declined to appear as co-author. I had to agree, reluctantly, and I thank him warmly for the stimulating cooperation. I have also benefitted from helpful discussions with Jean-François Mertens and Edi Karni. I assume sole responsibility for the contents.
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Dreze, J.H. Nested identification of subjective probabilities. SERIEs 3, 259–271 (2012). https://doi.org/10.1007/s13209-011-0049-4
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DOI: https://doi.org/10.1007/s13209-011-0049-4