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

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.