We study the problem of obtaining an expected utility representation for a potentially incomplete preference relation over lotteriesby means of a set of von Neumann–Morgenstern utility functions. It is shown that, when the prize space is a compact metric space, a preference relation admits such a multi-utility representation provided that it satisfies the standard axioms of expected utility theory. Moreover, the representing set of utilities is unique in a well defined sense.
Expected utility theory without the completeness axiom
Maccheroni, Fabio;
2004
Abstract
We study the problem of obtaining an expected utility representation for a potentially incomplete preference relation over lotteriesby means of a set of von Neumann–Morgenstern utility functions. It is shown that, when the prize space is a compact metric space, a preference relation admits such a multi-utility representation provided that it satisfies the standard axioms of expected utility theory. Moreover, the representing set of utilities is unique in a well defined sense.
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