Epistemic Games: Public Announcements and Questions-and-Answers

Thomas ?gotnes

Dynamic epistemic logic describes the possible information-changingactions available to individual agents, and their knowledge pre- andpost conditions.  For example, public announcement logic describesactions in the form of public, truthful announcements. However, littleresearch so far has considered describing and analysing rationalchoice between such actions, i.e., predicting what rationalself-interested agents actually will or should do. Since the outcomeof information exchange ultimately depends on the actions chosen byall the agents in the system, and assuming that agents havepreferences over such outcomes, this is a game theoreticscenario. This is an interesting general research direction, combininglogic and game theory in the study of rational informationexchange. In the talk I will, in particular, focus on two particularcases in detail. First, I consider the case where available actionsare public announcements, and where each agent has a (typicallyepistemic) goal formula that she would like to become true. What willeach agent announce?  The truth of the goal formula also depends onthe announcements made by other agents, thus we have a game-theoreticscenario.  I discuss how such *public announcement games* can beanalysed. Second, I consider the similar setting where instead ofchoosing an announcement each player chooses a question the otherplayer is obliged to truthfully answer. What are the best questions toask? Again, this question can be discussed by analysing the resulting*question-answer games*. The talk is based on joint work with Johan van Benthem, Hans van Ditmarsch and Stefan Minica.