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Threshold Value: How Binding Thresholds Affect the Outcome of a Negotiation


  • Sylvie Thoron, Université Paris-Est Créteil Val de Marne, 61 avenue du Général de Gaulle, 94010 Créteil Cedex, France and GREQAM, Centre de la Vieille Charité, 2 rue de la Charité, 13002 Marseille, France.

  • The author would like to thank Gérard Hamiache, Eric Maskin, Hervé Moulin, Jorgen Weibull, the participants in the economics seminar at the IAS in Princeton and the participants in the CTN conference in Paris for helpful discussions and comments on previous versions of the paper. She is particularly grateful to an anonymous referee whose comments and suggestions helped to improve this paper substantially.


The objective of this paper is to give the prospective outcome or “prospect” of a negotiation when the players’ value can only be realized if a certain threshold is reached. A threshold is usually defined as a certain total level of contribution. Here, I define a threshold in a cooperative game by the players who are necessary to reach it. It can take different forms such as a certain number of players, or certain coalitions of players. An important example is the minimum participation constraint in international environmental agreements. A value is proposed, which is defined for a given game and a given threshold. The threshold players may bear a commitment cost which decreases the benefit they can obtain from the negotiation.