Direct Implementation with Evidence

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 <cite>BL2012</cite>. 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 <cite>KT2012</cite>, 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.