This paper links coalition theory with matching mechanisms in the presence of global public goods among heterogeneous players. This matching coalition may achieve Pareto-improving outcomes while avoiding side payments. The paper characterizes conditions of coalition profitability and stability at both interior and corner equilibria. It is generally much harder to satisfy stability conditions than profitability conditions. A matching coalition is more profitable but less stable with a larger matching rate. Empirically there is no stable coalition but this can be overcome by introducing reputation mechanisms. There always exists a stable grand matching coalition if players value their reputation. The matching coalition faces a trade-off between matching depth and breadth.