Voluntary Contribution to Multiple Public Projects.

The problem of financing a set of public goods (facilities, projects) by private contributions is studied. The corresponding cooperative game, the realization game, is shown to be convex. For the noncooperative setting we study a realization scheme that induces a strategic game. This contribution game is shown to be best-response equivalent with a coordination game in which the payoff to all players is the utilitarian collective welfare function, i.e., the sum of the utility functions of the players. Several equilibrium properties are derived: no money is wasted in an equilibrium; a player whose necessary projects are not all realized does not contribute. Strategy profiles maximizing utilitarian welfare are strong Nash equilibria of the contribution game. Each strong Nash equilibrium corresponds to a core element of the realization game in a natural way. It is shown that there is a one-to-one correspondence between the set of strong Nash equilibria of the contribution game and the largest set of core elements of the realization game, that is consistent with maximizing the number of players with non-zero payoffs. It is precisely the subset of the core according to which rewards zero indicate null players.