Robust virtual implementation

• 成果类型: Article
• 署名作者: Bergemann, Dirk; Morris, Stephen
• 署名单位: Yale University; Princeton University
• 刊物名称: THEORETICAL ECONOMICS
• ISSN/ISSBN: 1555-7561
• 发表日期: 2009-03-01
• 页码: 45-88
• 关键词: Mechanism design; virtual implementation; robust implementation; rationalizability; ex post incentive compatibility

摘要

In a general interdependent preference environment, we characterize when two payoff types can be distinguished by their rationalizable strategic choices without any prior knowledge of their beliefs and higher order beliefs. We show that two payoff types are strategically distinguishable if and only if they satisfy a separability condition. The separability condition for each agent essentially requires that there is not too much interdependence in preferences across agents. A social choice function, mapping payoff type profiles to outcomes, can be robustly virtually implemented if there exists a mechanism such that every equilibrium on every type space achieves an outcome that is arbitrarily close to the outcome generated by the social choice function. This definition is equivalent to requiring virtual implementation in iterated deletion of strategies that are strictly dominated for all beliefs. The social choice function is robustly measurable if strategically indistinguishable payoff types receive the same allocation. We show that ex post incentive compatibility and robust measurability are necessary and sufficient for robust virtual implementation.