On a class of threshold public goods games : with applications to voting and the Kyoto Protocol

The launch of a public project requires support from "enough" members of a group. Members (players) are differently important for the project and have different cost/benefit relations. There are players who profit and players who suffer from the launch of the project. Examples are the Kyoto protocol, voting with different weights (shareholders, the UN with the veto power of the Security Council members), and international scientific or military expeditions. As coordination on one of the usually many pure strategy equilibria is difficult, mixed strategy equilibria are the focus of this investigation. If all players profit from the launch of the project then, despite the "unnecessary" costs, the requirement of full contributions is a Pareto-improvement to every original threshold. The contribution probabilities of some player types defined by their importance are characterized according to their cost/benefit relations.