B\"orgers's Open Question Resolved

Abstract

Focusing on stochastic finite-action mechanisms, we study implementation in undominated strategies and iteratively undominated strategies. We establish both possibility and impossibility results that resolve the open question in B\"orgers (1995). Contrary to the conventional understanding that positive results on Nash implementation need separability, quasilinearity, or infinite action sets, we provide -- to our knowledge -- the first positive result beyond those demanding assumptions.