# Laboratory Games and Quantum Behaviour: The Normal Form with a Separable State Space

Working paper
Author/s:
Peter J. Hammond
Issue number:
969
Publisher:
University of Warwick
Year:
2011
The subjective expected utility (SEU) criterion is formulated for a particular four-person “labo- ratory game” that a Bayesian rational decision maker plays with Nature, Chance, and an Experi- menter 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.
Developed by Paolo Gittoi