Direct Implementation with Evidence

TL;DR

This paper characterizes when social choice functions are Nash implementable with evidence in environments with bounded utilities, introducing a novel classification of lies and establishing conditions for implementation and renegotiation-proof contracts.

Contribution

It provides a complete characterization of Nash implementation with evidence, including new classifications of lies and conditions for bilateral contracts in environments with evidentiary costs.

Findings

Nash implementability characterized by measurability condition.

Implementation with two agents accounting for mixed strategies and evidentiary costs.

Necessary and sufficient conditions for renegotiation-proof bilateral contracts.

Abstract

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.