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Evolutionary implementation in aggregative games. (English) Zbl 1459.91009

Summary: Due to externalities, the equilibrium behavior in aggregative games is not efficient in the sense of maximizing aggregate payoff. We characterize conditions such that efficiency can be globally implemented in such games under evolutionary dynamics. If payoffs satisfy certain important concavity conditions, then the aggregate payoff function of these games has a unique maximizer. Once the planner imposes a transfer equal to the externality generated by agents, we obtain a new externality adjusted game. This is a potential game with the aggregate payoff function of the original game being its potential function. Evolutionary dynamics converge globally to the maximizer of this potential function, thereby implementing efficiency in the original game. Our earlier paper on public goods [the authors, J. Econ. Theory 181, 423–460 (2019; Zbl 1411.91087)] emerges as an example of the present general analysis. Two new applications are public bads and the tragedy of the commons.

MSC:

91A14 Potential and congestion games
91A22 Evolutionary games
91B18 Public goods

Citations:

Zbl 1411.91087
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References:

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