Implementation in economies with a Continuum of Agents
We study a general implementation problem for exchange economies with a continuum of players and private information, and test the robustness of the results for sequences of approximating finite economies. Assuming that the designer knows the distribution of the characteristics in the economy we consider continuous and unique implementation in both its equilibrium and dominant strategies versions and obtain results for general self-selective (first- and second-best) allocations. An upper hemicontinuity property of Bayesian equilibria of approximating economies for continuous mechanisms is demonstrated. Using this, we can, for example, conclude that if a given continuous mechanism implements uniquely a Walrasian allocation in the continuum economy then all Bayesian equilibria of large approximation economies will (with probability close to one) yield an allocation which is almost ex-post Pareto optimal.
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