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Equilibrium Solution in a Game between a Cooperative and its Members


  • Cesarino Bertini

    () (University of Bergamo, Department of Mathematics, Statistics, Informatics and Applications, Bergamo, Italy)

  • Gianfranco Gambarelli

    () (University of Bergamo, Department of Mathematics, Statistics, Informatics and Applications, Bergamo, Italy)

  • Antonino Scarelli

    () (University of Tuscia, Department of Ecology and Sustainable Economic Development, Viterbo, Italy)

  • Zoltán Varga

    () (Szent István University, Institute of Mathematics and Informatics, Gödöllö, Hungary)


In the paper a game-theoretical model is set up to describe the conflict situation in which the members of a marketing cooperative may take advantage of an external market price, higher than that offered by the cooperative. Under appropriate conditions on the penalty strategy of the cooperative, the faithfulness of all members will provide a Nash equilibrium for the considered game, which at the same time also is an attractive solution, with the cooperative as a distinguished player.

Suggested Citation

  • Cesarino Bertini & Gianfranco Gambarelli & Antonino Scarelli & Zoltán Varga, 2011. "Equilibrium Solution in a Game between a Cooperative and its Members," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 5(2), pages 162-171, August.
  • Handle: RePEc:fau:aucocz:au2011_162

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    References listed on IDEAS

    1. Paul B. Simpson, 1969. "On Defining Areas of Voter Choice: Professor Tullock on Stable Voting," The Quarterly Journal of Economics, Oxford University Press, vol. 83(3), pages 478-490.
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    4. Donald Saari, 2006. "Which is better: the Condorcet or Borda winner?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(1), pages 107-129, January.
    5. anonymous, 1982. "Communication," Management Science, INFORMS, vol. 28(3), pages 337-337, March.
    6. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-1041, November.
    7. Young, H. P., 1974. "An axiomatization of Borda's rule," Journal of Economic Theory, Elsevier, vol. 9(1), pages 43-52, September.
    8. Moulin, Herve, 1988. "Condorcet's principle implies the no show paradox," Journal of Economic Theory, Elsevier, vol. 45(1), pages 53-64, June.
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    Cited by:

    1. Vito Fragnelli & Gianfranco Gambarelli, 2014. "Further open problems in cooperative games," Operations Research and Decisions, Wroclaw University of Technology, Institute of Organization and Management, vol. 4, pages 51-62.

    More about this item


    Cooperatives; Game Theory; Nash equilibria;

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • Q13 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Agriculture - - - Agricultural Markets and Marketing; Cooperatives; Agribusiness


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