Participation constraints of matching mechanisms

Matching mechanisms have been proposed to improve public good provision in voluntary contributions. However, such decentralized subsidizing mechanisms may not be Pareto-improving and may suffer from incomplete information and incredible commitment. This paper examines participation constraints of matching mechanisms, and investigates the existence condition of Pareto-improving outcomes of small matching schemes, and characterizes the condition of desirable matching schemes. Income distributions across players play an important role. If the income distribution ensures an interior equilibrium, there always exist small Pareto-improving matching schemes regardless of preferences. This universal existence is useful for cooperation among heterogeneous players in the context without global information of preferences or at the international level without central governments. However, if the income inequality induces a corner equilibrium, matching schemes work in different ways and have different welfare effects in certain cases, and the existence of Pareto-improving matching schemes is not universal but is possible under a certain condition. In particular, if the corner player unilaterally matches the interior player, both players can be better off, indicating that unilateral action through matching can possibly generate Pareto-improving outcomes.