🤖 AI Summary
This paper studies robust mechanism design for persuasion games without prior probability assumptions. Addressing the core challenge that the receiver’s action must depend robustly on the sender’s experiment and signal—not on an unknown state prior—we propose a three-component robust mechanism: (i) incentivizing full revelation of the experiment, (ii) restricting decisions to depend solely on the posterior distribution, and (iii) imposing strict penalties for pooling deviations. We establish, for the first time, necessary and sufficient conditions for prior-independent implementability under ordinal preference uncertainty. We prove that, in binary-action settings, only ordinal-monotone allocation rules are robustly implementable. We provide a novel informational foundation for the deferred-acceptance algorithm. Finally, we extend our framework to environments with externalities and state-dependent outside options, showing that all efficient allocations are robustly implementable.
📝 Abstract
We analyze prior-free predictions in the design of persuasion games: settings where Receiver contracts their action on Sender's choices of experiment and realized signals about some state. To do so, we characterize robust mechanisms - those which induce the same allocation rules (mappings from the state to actions) regardless of prior beliefs. These mechanisms take a simple form: they (1) incentivize fully revealing experiments, (2) depend only on the induced posterior, and (3) maximally punish pooling deviations. We then highlight a tight connection between ordinal preference uncertainty and prior-dependent predictions - all such rules are implementable if and only if the sender has a state-independent least favorite action. This, in turn, implies all (and only) ordinally monotone allocation rules are robust in binary action problems. We apply our model to school choice and uncover a novel informational justification for deferred acceptance when school preferences depend on students' unknown ability. Finally, we study good allocation settings with externalities and state-dependent outside options and show all efficient allocation rules are robust, even with significant preference heterogeneity.
