Revenue Equivalence of the Volunteer’s Dilemma and the Stag Hunt Game and Inferiority of Intermediate Thresholds

The launch of a public project requires “enough” support from a group of n players. If players have only binary decision sets (participate or not, vote approvingly or not) this game is called a Binary Threshold Public Goods game (BTPG). In this paper we keep the individual cost/benefit ratios of all players constant and vary only the (rather generally defined) threshold. The revenues of the various BTPG equilibria are compared. Applying two principles of equilibrium selection, the least and the most demanding threshold, namely “one supporting player is sufficient” (Volunteer’s Dilemma) and “support by all players is necessary” (Stag Hunt game) are revenue equivalent for all players. Compared with the Stag Hunt game, all intermediate thresholds are connected with Pareto-inferior revenues.