Virtual Implementation in Nash Equilibrium
刻画了两人社会选择函数可虚拟实施的充要条件，条件简单且与精确实施形成对比，并展示了如何将结果扩展到严格纳什均衡、联盟-proof纳什均衡及基数偏好环境。
The two-person case needs to be considered separately. We provide a complete characterization of virtually implementable two-person social choice functions. While not all two-person social choice functions are virtually implementable, our necessary and sufficient condition is simple. This contrasts with the rather complex necessary and sufficient conditions for exact implementation. We show how our results can be extended to implementation in strict Nash equilibrium and coalition-proof Nash equilibrium, to social choice correspondences which map from cardinal preference profiles to lotteries, and to environments with a continuum of pure alternatives.