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A Bayesian implementable social choice function may not be truthfully implementable

Wu, Haoyang (2016): A Bayesian implementable social choice function may not be truthfully implementable.

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Abstract

The revelation principle is a fundamental theorem in many economics fields. In this paper, I construct an example to show that a social choice function which can be implemented in Bayesian Nash equilibrium is not truthfully implementable. The key point is the cost condition given in Section 2.3: agents pay cost when carrying out strategies in the indirect mechanism, but will not pay cost in the direct mechanism by definition. As a result, the revelation principle may not hold when agents' strategies are costly in the indirect mechanism.

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