Direct implementation with evidence

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We study full implementation with evidence in an environment with bounded utilities. We show that a social choice function is Nash implementable in a direct revelation mechanism if and only if it satisfies the measurability condition proposed by Ben‐Porath and Lipman (2012). Building on a novel classification of lies according to their refutability with evidence, the mechanism requires only two agents, accounts for mixed‐strategy equilibria, and accommodates evidentiary costs. While monetary transfers are used, they are off the equilibrium and can be balanced with three or more agents. In a richer model of evidence due to Kartik and Tercieux (2012a), we establish pure‐strategy implementation with two or more agents in a direct revelation mechanism. We also obtain a necessary and sufficient condition on the evidence structure for renegotiation‐proof bilateral contracts, based on the classification of lies.