Abstract
This paper introduces a novel channel of belief updating with awareness. Awareness is reflected by agents having state dependent subjective state spaces. An agent forms conjectures of his subjective state spaces in different states. He updates his belief over the true state by excluding states in which his conjectured subjective state spaces differ from his current state space. We restrict agents' capacities of belief updating through this channel by imposing axioms over agents' possible conjectures. We further use this framework to analyze belief updating when an agent's subjective state space expands. Importantly, in this framework the belief process is not necessarily a martingale. We use persuasion games as examples to illustrate this point. Since the receiver's belief process may not be a martingale, the sender might be better off sending an awareness signal to expand the receiver's state space than performing any feasible Bayesian experiment.
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