Hierarchical hypergames and Bayesian games: A generalization of the theoretical comparison of hypergames and Bayesian games considering hierarchy of perceptions

This paper discusses the relationship of two independently developed models of games with incomplete information, hierarchical hypergames and Bayesian games. It can be considered as a generalization of the previous study on the theoretical comparison of simple hypergames and Bayesian games (Sasaki and Kijima, 2012) by taking into account hierarchy of perceptions, i.e., an agent's perception about the other agents' perceptions, and so on. The authors first introduce the general way of transformation of any hierarchical hypergames into corresponding Bayesian games, which was called as the Bayesian representation of hierarchical hypergames. The authors then show that some equilibrium concepts for hierarchical hypergames can be associated with those for Bayesian games and discuss implications of the results.