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Evolutionary Implementation in Aggregative Games

  • Economics Discussion Papers
  • September 2, 2020
  • Ratul Lahkar,
  • Ratul Lahkar, Saptarshi Mukherjee

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 (Lahkar and Mukherjee [16]) emerges as an example of the present general analysis. Two new applications are public bads and the tragedy of the commons.

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