This note considers the core of a game for an economy with a public good subject to crowding and its relationships to the Lindahl equilibria of that economy. Crowding means here that cost functions for providing the public good are nondecreasing with respect to a group of agents, namely its size, in which the public good is produced and consumed collectively excluding any of the nonmembers. This treatment of crowding is similar to that of Ellickson,with which he presented examples that the Lindahl equilibrium does not belong to the core and that the core itself is empty, contrary to the assertion of Foley for the pure public good case. Crowding in this setting should involve a partition of agents into several “sharing groups”for the public good. Thus, in our game, players in each coalition are allowed to form a partition so as to maximize the net benefit of the coalition as a whole. We derive a necessary and sufficient condition for the game to have anonempty core, and a sufficient condition in a special case for the core to contain the Lindahl equilibria.
A Note on Lindahl Equilibria and the Core of a Game with a Crowded Public Good
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