Strategic Signaling Under Higher-order Inference

Abstract

Inferring the information structure of other agents is necessary to derive optimal mechanisms/signaling strategies in games with communications. However, in many real-world problems such as fake news detection, drug development, and lobbying, the (Bayesian) belief updating procedure is not one-shot, and agents' optimal signaling strategies rely on the responses of sequentially updated beliefs. This demands approaches to systematically analyze higher-order inference of agents and derive each agent's optimal manipulation of information revelation to serve her own objective. However, since the information space's size grows exponentially with the order of inference, approaches that serve both purposes can be complicated and hard to analyze. In order to advance the theoretical understanding of higher-order inference in games with communications, this thesis studies several models in social learning and information design and solves particular questions. First, we present an elegant approach to accumulate information under higher-order inference among agents in social learning models, and then explicitly construct an algorithm to achieve asymptotic learning. Second, we study two Bayesian persuasion problems, one with sequentially conducted experiments and the other with the receiver's action constrained exogenously. We propose a dynamic programming algorithm for the optimal commitments in the former problem and prove that the receiver benefits from constraints under binary-state models in the latter problem. These results highlight the fragility of optimal signaling strategies under higher-order inference. Last, we study information design problems where each sender only obtains partial information, and our results highlight the significance of the order of commitment under higher-order inference.