TITLE: Knowledge Games

ABSTRACT: The subject of epistemic logic is firmly entrenched in game theory, including the analysis of common knowledge and of public announcements, such as in `hat problems'. Analysis of communications to subgroups of the public, and the effects of such common knowledge of a subgroup on the information state of a larger group, is now a major research topic, with potential applications to distributed systems and computer security. Knowledge games are introduced to provide a comfortably concrete framework for the study of such interactions. We introduce the concepts of knowledge game, deal of cards, knowledge game state, game action, and action execution. A deal of cards is a function from cards to players. A knowledge game state is represented by a pointed multi-agent S5 model on the set of card deals where all players hold the same number of cards as in the actual deal. A game action combines a question with an answer, and is represented by a pointed multi-agent S5 frame on the set of possible answers. The execution of a game action in a knowledge game state corresponds to the computation of a pointed multi-agent S5 model that is a restriction of the direct product of the corresponding action frame and game model. Game actions can be described by knowledge actions in a dynamic epistemic language: to each action corresponds a dynamic operator. We introduce the language and give some examples of actions.