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Mazur, J.E. (1987) An Adjusting Procedure for Studying Delayed Reinforcement. In: Commons, M.L., Mazur, J.E., Nevin, J.A. and Rachlin, H., Eds., Quantitative Analysis of behavior: Vol. 5. The Effect of Delay and of Intervening Events of Reinforcement Value, Erlbaum, 55-73.

has been cited by the following article:

• TITLE: A Note on the Relationship of Normative Principles between Decision under Risk and over Time

  AUTHORS: Taiki Takahashi

  KEYWORDS: Behavioral Economics, Risk, Uncertainty, Hyperbolic Discounting

  JOURNAL NAME: Applied Mathematics, Vol.16 No.11, November 4, 2025

  ABSTRACT: Recent advances in behavioral economics elucidated a number of deviations of actual human decisions and choices from mathematical principles of normative decision theory in neoclassical economics. This study demonstrates, by utilizing the mathematical model of probability discounting theory in behavioral psychology, that normative principles of decision making under risk (von Neumann and Morgenstern’s expected utility theory) and over time (dynamic consistency, i.e., exponential discounting) are incompatible. Possible future applications of this finding in behavioral economics and quantum epistemics are discussed.