The bulletin of mathematical biophysics

, Volume 9, Issue 3, pp 109–122 | Cite as

Forms of output distribution between two individuals motivated by a satisfaction function

  • Anatol Rapoport


Motivations of two individuals governed by a satisfaction function are assumed to determine their respective “efforts”, which result in the production of “output”, i.e., objects of satisfaction. In previous papers the sharing of output was prescribed in advance. In the present article, however, the sharing formula itself is determined to a certain extent by the satisfaction function. The rate of remuneration per unit of output for each individual is taken to be proportional to the derivative of the satisfaction of the other individual with respect to the effort of the first. The formulation of this condition leads to a partial differential equation whose solutions determine the sharing formula. Sharing determined in this way is referred to as sharing according to the Condition of Mutual Need (C.M.N.). Satisfaction resulting from five different situations are the computed and compared: (1) an individual producing and consuming alone; (2) two individuals sharing equally and neither taking the “initiative” to determine the optimum output; (3) sharing determined by C.M.N. with optimum output determined as in (2); (4) equal sharing but with one individual taking “initiative” in determining optimal output; and (5) sharing determined by C.M.N. and optiml output by the “initiative” of one individual. further considerations concern conditions imposed on the arbitrary function occurring in the solution of the above-mentioned partial differential equation.


Optimal Output Output Distribution Mathematical Biophysics Motivation Interaction Final Satisfaction 
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  1. Rapoport, A. 1947a. “Mathematial Theory of Motivation Interactions of Two Individuals: I”.Bull. Math. Biophysics,9, 17–28.CrossRefGoogle Scholar
  2. Rapoport, A. 1947b. “Mathematical Theory of Motivation in Interaction of Two Individuals: II”.Bull. Math. Biophysics,9, 41–61.MathSciNetCrossRefGoogle Scholar
  3. Rashevsky, N. 1947. “A Problem in Mathematical Biophysics of Interaction of Two or More Individuals Which May Be of Interest in Mathematical Sociology”.Bull. Math. Biophysics,9, 9–15.CrossRefGoogle Scholar
  4. Thurstone, L. L. 1931. “The Indifference Function”.Jour. Social Psychol.,2, 139–167.CrossRefGoogle Scholar

Copyright information

© The University of Chicago Press 1947

Authors and Affiliations

  • Anatol Rapoport
    • 1
    • 2
  1. 1.Section of Mathematical BiophysicsThe University of ChicagoChicagoUSA
  2. 2.Department of MathematicsIllinois Institute of TechnologyUSA

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