What will they say?—Public Announcement Games

Abstract

Dynamic epistemic logic describes the possible information-changingactions available to individual agents, and their knowledge pre- and post conditions.For example, public announcement logic describes actions in the form of public,truthful announcements. However, little research so far has considered describing andanalysing rational choice between such actions, i.e., predictingwhat rational self-interestedagents actually will or should do. Since the outcome of information exchangeultimately depends on the actions chosen by all the agents in the system, and assumingthat agents have preferences over such outcomes, this is a game theoretic scenario.This is, in our opinion, an interesting general research direction, combining logic andgame theory in the study of rational information exchange. In this article we take somefirst steps in this direction: we consider the case where available actions are publicannouncements, and where each agent has a (typically epistemic) goal formula thatshe would like to become true. What will each agent announce? The truth of the goalformula also depends on the announcements made by other agents. We analyse suchpublic announcement games.