Subjective expected utility with a spectral state space View Full Text


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Article Info

DATE

2019-01-14

AUTHORS

Marcus Pivato

ABSTRACT

An agent faces a decision under uncertainty with the following structure. There is a set A of “acts”; each will yield an unknown real-valued payoff. Linear combinations of acts are feasible; thus, A is a vector space. But there is no pre-specified set of states of nature. Instead, there is a Boolean algebra I describing information the agent could acquire. For each element of I, she has a conditional preference order on A. I show that if these conditional preferences satisfy certain axioms, then there is a unique compact Hausdorff space S such that elements of A correspond to continuous real-valued functions on S, elements of I correspond to regular closed subsets of S, and the conditional preferences have a subjective expected utility (SEU) representation given by a Borel probability measure on S and a continuous utility function. I consider two settings; in one, A has a partial order making it a Riesz space or Banach lattice, and I is the Boolean algebra of bands in A. In the other, A has a multiplication operator making it a commutative Banach algebra, and I is the Boolean algebra of regular ideals in A. Finally, given two such vector spaces A1 and A2 with SEU representations on topological spaces S1 and S2, I show that a preference-preserving homomorphism A2⟶A1 corresponds to a probability-preserving continuous function S1⟶S2. I interpret this as a model of changing awareness. More... »

PAGES

1-65

References to SciGraph publications

  • 2009. A Course in Commutative Banach Algebras in NONE
  • 2012-10. Expanding state space and extension of beliefs in THEORY AND DECISION
  • 2013-08. Awareness-dependent subjective expected utility in INTERNATIONAL JOURNAL OF GAME THEORY
  • 1991. Banach Lattices in NONE
  • 1990. Expected Utility and Mathematical Expectation in UTILITY AND PROBABILITY
  • 1964-09. Real banach algebras in ARKIV FÖR MATEMATIK
  • 2015-06. Probabilistic sophistication and reverse Bayesianism in JOURNAL OF RISK AND UNCERTAINTY
  • 2008-06. On the existence of expected multi-utility representations in ECONOMIC THEORY
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