By designing an information structure, which is a probability distribution over the set of signals, an information designer tries to induce her preferred distribution over action profiles by the players. This paper characterizes outcomes, probabilistic distribution on actions by a player, implemented by this information design problem under some robustness considerations. In particular, we require the implemented outcomes to be robust to a small misspecification of the players' belief hierarchies generated by the information structure. In other words, in the nearby information structure, the outcomes closed to the original one should be implementable. To formalize this idea, the paper also proposes a concept of a distance between information structures. Robustly implementable outcome is strictly dominant for all realizations of the signal. This necessary and sufficient condition severely restricts the information designer's ability to influence players' decisions. In some cases, the designer cannot be better off by manipulating information. The designer also has to provide more informative signals in the robust problem than the standard one.
This paper defines the notion of interim correlated rationalizability in the very general class of games with incomplete information. Working with the Epstein-Wang universal type space, our framework is general enough to accommodate non-expected utility models and ambiguity averse players. Interim correlated rationalizability is a natural generalization of the rationalizability concept in the expected utility case and properties of the concept are studied. In particular, our rationalizability concept characterizes rationality and common knowledge of rationality. Furthermore, we investigate robustness to higher order uncertainty. Interim correlated rationalizability is the strongest solution concept satisfying upper hemicontinuity in the universal type space. Moreover, any rationalizable action can be made uniquely rationalizable by perturbing higher order uncertainty. As is the case for the expected utility model, the rationalizable action profile is generically unique even though ambiguity aversion must weakly enlarge the rationalizable set. Finally, we show that interim correlated rationalizability is generically robust to the ambiguity.
We will introduce a new sufficient condition for social choice correspondences to be fully implementable in mixed-Nash equilibrium called strong set-monotonicity in the case where there are more than three persons. We will show that strong set-monotonicity is also a necessary condition if the domain of the preferences is sufficiently large. Our characterization does not involve the condition of no veto power. Thus, our result can be applied to many important problems to which the traditional approach using no veto power cannot be applied. Those problems include market design or matching problems. We will prove that some interesting matching rules are implementable in mixed-Nash equilibrium while they are not implementable in pure strategy Nash equilibrium.
We will provide a necessary and sufficient condition for social choice correspondences to be implementable in mixed-Nash equilibrium. We mainly focus on the case where there are exactly two agents. The two-agent models are relevant for many applications including bargaining and contracting. We also derive a couple of important implications on mixed-Nash implementable social choice correspondences from our conditions. Among others, we show that non-dictatorial and efficient correspondences are implementable even when there are exactly two agents while those correspondences are not implementable in the pure strategy Nash equilibrium case.
Ambiguity in Robust Mechanism Design
Admissibility in Regular Preference Form Games
