Ollar, Mariann and Penta, Antonio (2024) Incentive Compatibility and Belief Restrictions. TSE Working Paper, n. 24-1558, Toulouse

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Abstract

We study a framework for robust mechanism design that can accommodate
various degrees of robustness with respect to agents’ beliefs, and which includes
both the belief-free and Bayesian settings as special cases. For general
belief restrictions, we characterize the set of incentive compatible direct mechanisms in general environments with interdependent values. The necessary
conditions that we identify, based on a first-order approach, provide a unified
view of several known results, as well as novel ones, including a robust version
of the revenue equivalence theorem that holds under a notion of generalized
independence that also applies to non-Bayesian settings. Our main characterizations
informthe design of belief-based terms, in pursuit of various objectives
in mechanism design, including attaining incentive compatibility in environments
that violate standard single-crossing and monotonicity conditions. We
discuss several implications of these results. For instance, we show that, under weak conditions on the belief restrictions, any allocation rule can be implemented,
but full rent extraction need not follow. Information rents are generally
possible, and they decrease monotonically as the robustness requirements
are weakened.