Natural implementation with partially-honest agents in economic environments with free-disposal

We study Nash implementation by natural price-quantity mechanisms in pure exchange economies with free-disposal (Saijo et al., 1996, 1999) where agents have weak/strong intrinsic preferences for honesty (Dutta and Sen, 2012). Firstly, the Walrasian rule is shown to be non-implementable where all agents have weak (but not strong) intrinsic preferences for honesty. Secondly, the class of efficient allocation rules that are implementable is identified provided that at least one agent has strong intrinsic preferences for honesty. Lastly, the Walrasian rule is shown to belong to that class.