A mechanism of proportional contributions for public good games

Public good games in coalitional form, such as the ones depicting international environmental agreements for the reduction of a global pollutant, generally foresee scarce levels of cooperation. The incentive to free ride, that increases for higher levels of cooperation, prevents the formation of stable coalitions. The introduction of other–regarding preferences, in the form of Fehr and Schmidt utility functions, enlarges cooperation, but still at suboptimal levels. The present paper considers a further possibility, namely the introduction of a mechanism through which the contributions of players to the public good are proportional to the average contribution of the other players abiding to the mechanism: proportional contributions. The mechanism is therefore rooted into reciprocity. By applying it to a standard abatement game parameterized on the RICE model, we show that the mechanism is in fact able to increase cooperation both under standard and under F&S preferences. Stability of the grand coalition is never reached, but potential internally stable grand coalitions are achieved under F&S preferences. The attainment of higher cooperation comes at the expense of the level of global abatement that is lower when proportional contributions are in place.