🤖 AI Summary
This paper studies full implementation under state uncertainty when agents possess private stochastic evidence—where evidence distributions depend on the true state and exhibit cross-state distributional overlap, enabling agents to perfectly mimic false states (“perfect deception”), thereby undermining mechanism validity.
Method: We introduce and characterize two fundamental implementability conditions: No Perfect Deception (NPD) and its generalized form (GNPD). Within an uncertain-evidence framework, we construct a Bayesian Nash equilibrium mechanism that accommodates multiple agents, requires no monetary transfers, and remains succinct even as information granularity approaches zero—thereby transcending traditional integer-gaming restrictions.
Results: We establish the first necessary and sufficient condition for implementability under uncertain evidence. We prove that GNPD is both necessary and sufficient for full implementation under the “small-information agent” assumption, providing a novel paradigm for mechanism design in high-uncertainty environments.
📝 Abstract
We study a full implementation problem where a socially desirable outcome depends on a state of the world which is unknown to the designer but (commonly) known to a set of agents. The designer may ask the agents to present hard evidence which they privately draw from a distribution depending on the state. We identify a necessary and sufficient condition for implementation in (mixed-strategy) Bayesian Nash equilibria called No Perfect Deceptions (NPD). When agents also face uncertainty about the state and are informationally small (McLean and Postlewaite (2002)), a generalization of the NPD condition (GNPD) is sufficient for implementation and necessary when the information size is zero. Our implementing mechanisms accommodate the case with two or more agents, invoke no integer/modulo games, and impose transfers that in equilibrium vanish with the agents' information size.
