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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2209.10741 |
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| _version_ | 1866909723730640896 |
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| author | Banerjee, Soumen Chen, Yi-Chun |
| author_facet | Banerjee, Soumen Chen, Yi-Chun |
| contents | We study a full implementation problem with a state unknown to the designer but known to agents, where agents have uncertain evidence privately drawn from state-dependent distributions. Stochastic evidence enables ``perfect deceptions,'' where agents' reports can mimic the evidence distribution of a false state, making differentiation impossible for any mechanism. This yields our main result: a necessary and sufficient condition, No Perfect Deceptions (NPD), for implementation in (mixed-strategy) Bayesian Nash equilibria. The solution requires novel techniques like belief elicitation via competing scoring rules, and an endogenous ``test allocation'' using the evidence structure. For informationally small agents (McLean and Postlewaite (2002)), a generalized condition (GNPD) is sufficient. Our mechanisms work for two or more agents, avoid integer/modulo games, and use limited liability transfers that vanish in equilibrium. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_10741 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Implementation with Uncertain Evidence Banerjee, Soumen Chen, Yi-Chun Theoretical Economics We study a full implementation problem with a state unknown to the designer but known to agents, where agents have uncertain evidence privately drawn from state-dependent distributions. Stochastic evidence enables ``perfect deceptions,'' where agents' reports can mimic the evidence distribution of a false state, making differentiation impossible for any mechanism. This yields our main result: a necessary and sufficient condition, No Perfect Deceptions (NPD), for implementation in (mixed-strategy) Bayesian Nash equilibria. The solution requires novel techniques like belief elicitation via competing scoring rules, and an endogenous ``test allocation'' using the evidence structure. For informationally small agents (McLean and Postlewaite (2002)), a generalized condition (GNPD) is sufficient. Our mechanisms work for two or more agents, avoid integer/modulo games, and use limited liability transfers that vanish in equilibrium. |
| title | Implementation with Uncertain Evidence |
| topic | Theoretical Economics |
| url | https://arxiv.org/abs/2209.10741 |