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A Bayesian implementable social choice function cannot be implemented by a direct mechanism

Wu, Haoyang (2016): A Bayesian implementable social choice function cannot be implemented by a direct mechanism.

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Abstract

The revelation principle is a fundamental theorem in many economics fields such as game theory, mechanism design and auction theory etc. In this paper, I construct an example to show that a social choice function which can be implemented in Bayesian Nash equilibrium by an indirect mechanism cannot be implemented by a direct mechanism. The key point is that agents pay cost in the indirect mechanism, but pay nothing in the direct mechanism. As a result, the revelation principle does not hold when agent's cost cannot be neglected in the indirect mechanism.

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