Evolutionary implementation in a public goods game

We consider implementation of the efficient state in a large population public goods game. Due to positive externalities, the efficient state is different from the Nash equilibrium of the game. We apply a transfer scheme equal to the externality in the game. The externality adjusted public goods game is a potential game with a unique Nash equilibrium, which is the efficient state of the original game. It is also a continuous–strategy aggregative game. We introduce the best response dynamic for such aggregative potential games to show evolutionary implementation. Agents converge to the efficient state under this dynamic in the externality adjusted game. We extend this result to other prominent evolutionary dynamics. The pure externality price scheme, however, causes a budget deficit. A modification of this scheme solves this problem while evolutionarily implementing efficiency.