Stealthy Deception in Hypergames Under Informational Asymmetry

This paper considers games of incomplete information, where one player (the deceiver) has an informational advantage over the other (the mark) and intends to employ it for belief manipulation. We use the formalism of hypergames to represent the asymmetric information available to players. This framework allows us to formalize various notions of belief manipulation that revolve around the idea of the deceiver being able to make the mark believe that a particular action has lost its advantageous character. In the case when the deceiver does not mind revealing information to the mark as the game evolves, we provide a necessary condition and a sufficient condition for deceivability. In the case when the deceiver acts in a stealthy way, i.e., restricts its actions to those that do not contradict the belief of the mark, we fully characterize when deception is possible and design to find a sequence of deceiving actions. Our correctness guarantees for this strategy are based on a precise characterization of the acyclic structure of subjective hypergames. An example illustrates our results.