Decomposable Choice Under Uncertainty

Simon Grant, Atsushi Kajii and Ben Polak ()
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Ben Polak: Cowles Foundation, Yale University, https://economics.yale.edu/people/faculty/benjamin-polak

No 1207, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: Savage motivated his Sure Thing Principle by arguing that, whenever an act would be preferred if an event obtains and preferred if that event did not obtain, then it should be preferred overall. The idea that it should be possible to decompose and recompose decision problems in this way has normative appeal. We show, however, that it does not require the full separability across events implicit in Savage's axiom. We formulate a weaker axiom that suffices for decomposability, and show that this implies an implicit additive representation. Our decomposability property makes local necessary conditions for optimality, globally sufficient. Thus, it is useful in computing optimal acts. It also enables Nash behavior in games of incomplete information to be decentralized to the agent-normal form. None of these results rely on probabilistic sophistication; indeed, our axiom is consistent with the Ellsberg paradox. If we assume probabilistic sophistication, however, then the axiom holds if and only if the agent's induced preferences over lotteries satisfy betweenness.

Keywords: Sure-thing principle; decomposability; uncertainty; computation; dynamic programming solvability; agent-normal form games; non-expected utility; betweenness (search for similar items in EconPapers)
JEL-codes: D80 D81 (search for similar items in EconPapers)
Pages: 33 pages
Date: 1999-01
Note: CFP 998.
References: View references in EconPapers View complete reference list from CitEc
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Published in Journal of Economic Theory (2000), 92(2): 169-197

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