Commutative Prospect Theory and Stopped Behavioral Processes for Fair Gambles

Cadogan, Godfrey (2010): Commutative Prospect Theory and Stopped Behavioral Processes for Fair Gambles.

Abstract

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: commutative prospect theory; homotopy; stopping time; behavioral stochastic process
• Subjects: D - Microeconomics > D0 - General > D03 - Behavioral Microeconomics: Underlying Principles; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D81 - Criteria for Decision-Making under Risk and Uncertainty; D - Microeconomics > D7 - Analysis of Collective Decision-Making > D70 - General; C - Mathematical and Quantitative Methods > C0 - General; C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods

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