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Commutative Prospect Theory and Stopped Behavioral Processes for Fair Gambles

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Version 2 2022-09-26, 15:13
Version 1 2021-05-21, 17:38
journal contribution
posted on 2022-09-26, 15:13 authored by Godfrey Cadogan

We augment Tversky and Khaneman (1992) (TK92) Cumulative Prospect Theory (CPT) function space with a sample space for states of nature, and depict a commutative map of behavior on the augmented space. In particular, we use a homotopy lifting property to mimic behavioral stochastic processes arising from deformation of stochastic choice into outcome. A psychological distance metric (in the class of Dudley-Talagrand inequalities) for stochastic learning, was used to characterize stopping times for behavioral processes. In which case, for a class of nonseparable space-time probability density functions, we find that behavioral processes are uniformly stopped before the goal of fair gamble is attained. Further, we find that when faced with a fair gamble, agents exhibit submartingale [supermartingale] behavior, subjectively, under CPT probability weighting scheme. We show that even when agents have classic von Neuman-Morgenstern preferences over probability distribution, and know that the gamble is a martingale, they exhibit probability weighting to compensate for probability leakage arising from the their stopped behavioral process. 

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