Laboratory Games and Quantum Behaviour: The Normal Form with a Separable State Space
The subjective expected utility (SEU) criterion is formulated for a particular four-person “laboratory game” that a Bayesian rational decision maker plays with Nature, Chance, and an Experimenter who influences what quantum behaviour is observable by choosing an orthonormal basis in a separable complex Hilbert space of latent variables. Nature chooses a state in this basis, along with an observed data series governing Chance's random choice of consequence. When Gleason's theorem holds, imposing quantum equivalence implies that the expected likelihood of any data series w.r.t. prior beliefs equals the trace of the product of appropriate subjective density and likelihood operators.
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- Jacob Gyntelberg & Frank Hansen, 2004.
"Expected utility theory with ”small worlds”,"
04-20, University of Copenhagen. Department of Economics, revised Jan 2005.
- Vladimir Ivanovitch Danilov & Ariane Lambert-Mogiliansky, 2008.
"Measurable systems and behavioral sciences,"
- V. Danilov & A. Lambert-Mogiliansky, 2010. "Expected utility theory under non-classical uncertainty," Theory and Decision, Springer, vol. 68(1), pages 25-47, February.
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