A refined utility function for modeling “me” vs. “us” allocation in a sequential group decision process

  • Dmitry Gimon
  • Alexandre Bevilacqua LeonetiEmail author
Original Article


Considering the psychological aspects of altruism and reciprocity in strategic interactions, we propose using the Cobb–Douglas utility function to refine standard utility functions as a weighted product of the player’s utility (“me” factor) and the jointly utility of players (“us” factor). We model an altruism willingness function to define the strategic allocation within “me” vs. “us” based on perceived kindness of the counterparts during the past agreements and unconditional altruism. Numerical examples are presented to show how the model represents the sequential group decision process of players with heterogeneous altruism profiles.


Multi-criteria Vector games Nash equilibrium Dynamic games Cobb–Douglas function 

Mathematics Subject Classification

91B10 91B16 



The authors acknowledge the anonymous reviewers for their significant suggestions for the improvement of this paper to the present version.


  1. Andreoni J (1990) Impure altruism and donations to public goods: a theory of warm-glow giving. Econ J 100(401):464–477CrossRefGoogle Scholar
  2. Cobb CW, Douglas PH (1928) A theory of production. Am Econ Rev 18:139–165Google Scholar
  3. Dufwenberg M, Kirchsteiger G (2004) A theory of sequential reciprocity. Games Econ Behav 47(2):268–298CrossRefGoogle Scholar
  4. Leoneti AB (2016) Utility Function for modeling group multicriteria decision making problems as games. Operat Res Perspect 3:21–26CrossRefGoogle Scholar
  5. Lotem A, Fishman MA, Stone L (2003) From reciprocity to unconditional altruism through signalling benefits. Proc R Soc Lond B Biol Sci 270(1511):199–205CrossRefGoogle Scholar
  6. Luce RD, Howard R (1957) Games and decisions: introduction and critical surveys. Wiley, New YorkGoogle Scholar
  7. McKelvey RD, McLennan AM, Turocy TL (2006) Gambit: software tools for game theory, version 16.0.1.
  8. Rabin M (1993) Incorporating fairness into game theory and economics. Am Econ Rev 1:1281–1302Google Scholar
  9. Trivers RL (1971) The evolution of reciprocal altruism. Q Rev Biol 46(1):35–57CrossRefGoogle Scholar
  10. Varian HR (1992) Microeconomic analysis. Norton & Company, New YorkGoogle Scholar

Copyright information

© EURO - The Association of European Operational Research Societies and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Park UniversityParkvilleUSA
  2. 2.Research Group in Decision Sciences, School of Economics, Business Administration and AccountingUniversity of São PauloRibeirão PretoBrazil

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