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Risk Sharing and Group Decision Making

Author

Listed:
  • Jehoshua Eliashberg

    (Northwestern University)

  • Robert L. Winkler

    (Indiana University and INSEAD)

Abstract

In a decision-making problem where a group will receive an uncertain payoff which must be divided among the members of the group, the ultimate payoff of interest is the vector of individual payoffs received by the members of the group. In this paper, preferences are quantified in terms of cardinal utility functions for such vectors of payoffs. These utility functions can represent preferences concerning "equitable" and "inequitable" vectors of payoffs as well as attitudes toward risk. The individual utility functions are aggregated to form a group utility function for the vector of payoffs, and this latter function is, in turn, used to generate a group utility function for the overall group payoff and a sharing rule for dividing the group payoff into individual payoffs. The resulting group decisions are Pareto optimal in utility space. Properties of the sharing rule and the group utility function are investigated for additive and multilinear group utility functions.

Suggested Citation

  • Jehoshua Eliashberg & Robert L. Winkler, 1981. "Risk Sharing and Group Decision Making," Management Science, INFORMS, vol. 27(11), pages 1221-1235, November.
    • Handle: RePEc:inm:ormnsc:v:27:y:1981:i:11:p:1221-1235
    DOI: 10.1287/mnsc.27.11.1221
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    Citations

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    Cited by:

    1. Lambrecht, Bart & Chen, Shiqi, 2019. "Financial Policies and Internal Governance with Heterogeneous Risk Preferences," CEPR Discussion Papers 13888, C.E.P.R. Discussion Papers.
    2. Eugenio Peluso & Alain Trannoy, 2012. "The Cake-eating problem: Non-linear sharing rules," Working Papers 26/2012, University of Verona, Department of Economics.
    3. Juzhi Zhang & Suresh P. Sethi & Tsan‐Ming Choi & T. C. E. Cheng, 2020. "Supply Chains Involving a Mean‐Variance‐Skewness‐Kurtosis Newsvendor: Analysis and Coordination," Production and Operations Management, Production and Operations Management Society, vol. 29(6), pages 1397-1430, June.
    4. Chang, Victor & Liu, Ben S.C. & Sudharshan, D. & Xu, Qianwen Ariel, 2021. "Towards an effective negotiation modeling: Investigating transboundary disputes with cases of lower possibilities," Technological Forecasting and Social Change, Elsevier, vol. 165(C).
    5. Kaynar, Nur & Karsu, Özlem, 2018. "Equitable decision making approaches over allocations of multiple benefits to multiple entities," Omega, Elsevier, vol. 81(C), pages 85-98.
    6. Zhang, Junyi & Kuwano, Masashi & Lee, Backjin & Fujiwara, Akimasa, 2009. "Modeling household discrete choice behavior incorporating heterogeneous group decision-making mechanisms," Transportation Research Part B: Methodological, Elsevier, vol. 43(2), pages 230-250, February.
    7. Xia Chen & Yucheng Dong & Ying He, 2024. "Group Risky Choice and Resource Allocation Under Social Comparison Effects," Group Decision and Negotiation, Springer, vol. 33(5), pages 977-1017, October.
    8. Radoslav Raykov, 2014. "Uncertain Costs and Vertical Differentiation in an Insurance Duopoly," Staff Working Papers 14-14, Bank of Canada.
    9. Joseph Kadane & Javier Girón & Daniel Peña & Peter Fishburn & Simon French & D. Lindley & Giovanni Parmigiani & Robert Winkler, 1993. "Several Bayesians: A review," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 2(1), pages 1-32, December.
    10. Zhang, Junyi & Timmermans, Harry J. P. & Borgers, Aloys, 2005. "A model of household task allocation and time use," Transportation Research Part B: Methodological, Elsevier, vol. 39(1), pages 81-95, January.
    11. Abel P. Jeuland & Steven M. Shugan, 2008. "Managing Channel Profits," Marketing Science, INFORMS, vol. 27(1), pages 52-69, 01-02.
    12. Min Ding & Jehoshua Eliashberg, 2008. "A Dynamic Competitive Forecasting Model Incorporating Dyadic Decision Making," Management Science, INFORMS, vol. 54(4), pages 820-834, April.
    13. James E. Smith & Detlof von Winterfeldt, 2004. "Anniversary Article: Decision Analysis in Management Science," Management Science, INFORMS, vol. 50(5), pages 561-574, May.

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