Implementing efficiency with equality

We consider the implementation of efficiency with minimum inequality in a large population model of negative externalities. Formally, the model is one of tragedy of the commons with the aggregate strategy at the efficient state being lower than at the Nash equilibrium. A planner can restore efficiency by imposing an externality equivalent tax and then redistributing the tax revenue as transfers to lower inequality. We characterize the payment scheme that minimizes inequality, as measured by the Gini coefficient, at the efficient state subject to incentive compatibility and budget balance. We then construct a mechanism that implements efficiency with minimum inequality in dominant strategies. We also show that minimizing inequality at the efficient state maximizes the minimum payoff at efficiency. However, it is not equivalent to implementing the Rawlsian social choice function.