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.