We expand the scope of the two-aggregate method by applying it to a situation where many heterogeneous players are free to contribute to both aggregates. Such situations naturally arise in various resource allocation problems. Hence our method is useful in many applications. A...

Matching mechanisms are regarded as an important instrument to bring about Pareto optimal allocations in a public good economy and to cure the underprovision problem associated with private provision of public goods. The desired Pareto optimal interior matching equilibrium, however, emerges only...