One important issue in mechanism design theory is to model agents’ behaviors under uncertainty. The classical approach assumes that agents hold commonly known probability assessments towards uncertainty, which has been challenged by economists in many fields. My thesis adopts alternative methods to model agents’ behaviors. The new findings contribute to understanding how the mechanism designer can benefit from agents’ uncertainty aversion and how she should respond to the lack of information on agents’ probability assessments.
Chapter 1 of this thesis allows the mechanism designer to introduce ambiguity to the mechanism. Instead of informing agents of the precise payment rule that she commits to, the mechanism designer can tell agents multiple payment rules that she may have committed to. The multiple payment rules are called ambiguous transfers. As agents do not know which rule is chosen by the designer, they are assumed to make decisions based on the worst-case scenario. Under this assumption, this chapter characterizes when the mechanism designer can obtain the first-best outcomes by introducing ambiguous transfers. Compared to the standard approach where the payment rule is unambiguous, first-best mechanism design becomes possible under a broader information structure. Hence, there are cases when the mechanism designer can benefit from introducing ambiguity.
Chapter 2 assumes that the mechanism designer does not know agents’ probability assessments about others’ private information. The mechanisms designed to implement the social choice function thus should not depend on the probability assessments, which are called robust mechanisms. Different from the existing robust mechanism design literature where agents are always assumed to act non-cooperatively, this chapter allows them to communicate and form coalitions. This chapter provides necessary and almost sufficient conditions for robustly implementing a social choice function as an equilibrium that is immune to all coalitional deviations. As there are social choice functions that are only implementable with coalitional structures, this chapter provides insights on when agents should be allowed to communicate. As an extension, when the mechanism designer has no information on which coalitions can be formed, this chapter also provides conditions for robust implementation under all coalition patterns.
Chapter 3 assumes that agents are not probabilistic about others’ private information. Instead, when they hold ambiguous assessments about others’ information, they make decisions based on the worst-case belief. This chapter provides necessary and almost sufficient conditions on when a social choice goal is implementable under such a behavioral assumption. As there are social choice goals that are only implementable under ambiguous assessments, this chapter provides insights on what information structure is desirable to the mechanism designer.