Success rates in simplified threshold public goods games - a theoretical model

This paper develops a theoretical model based on theories of equilibrium selection in order to predict success rates in threshold public goods games, i.e., the probability with which a group of players provides enough contribution in sum to exceed a predefined threshold value. For this purpose, a prototypical version of a threshold public goods game is simplified to a 2 x 2 normal-form game. The simplified game consists of only one focal pure strategy for positive contributions aiming at an efficient allocation of the threshold value. The game's second pure strategy, zero contributions, represents a safe choice for players who do not want to risk coordination failure. By calculating the stability sets of these two pure strategies, success rates can be put in explicit relation to the game parameters. It is also argued that this approach has similarities with determining the relative size of the strategies' basins of attraction in a stochastic dynamical system (cf. Kandori, Mailath, and Rob, 1993, Econometrica, Vol. 61, p. 29-56).