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Implementation with Uncertain Evidence

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  • Soumen Banerjee
  • Yi-Chun Chen

Abstract

We study a full implementation problem with hard evidence where the state is common knowledge but agents face uncertainty about the evidence endowments of other agents. We identify a necessary and sufficient condition for implementation in mixed-strategy Bayesian Nash equilibria called No Perfect Deceptions. The implementing mechanism requires only two agents and a finite message space, imposes transfers only off the equilibrium, and invoke no device with "...questionable features..." such as integer or modulo games. Requiring only implementation in pure-strategy equilibria weakens the necessary and sufficient condition to No Pure-Perfect Deceptions. In general type spaces where the state is not common knowledge, a condition called higher-order measurability is necessary and sufficient for rationalizable implementation with arbitrarily small transfers alongside.

Suggested Citation

  • Soumen Banerjee & Yi-Chun Chen, 2022. "Implementation with Uncertain Evidence," Papers 2209.10741, arXiv.org.
    • Handle: RePEc:arx:papers:2209.10741
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    References listed on IDEAS

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    Cited by:

    1. Banerjee, Soumen & Chen, Yi-Chun & Sun, Yifei, 2024. "Direct implementation with evidence," Theoretical Economics, Econometric Society, vol. 19(2), May.

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