Dynamic epistemic logic describes the possible information-changing actions 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 and analysing rational choice between such actions, i.e., predicting what rational self-interested agents actually will or should do. Since the outcome of information exchange ultimately depends on the actions chosen by all the agents in the system, and assuming that agents have preferences over such outcomes, this is a game theoretic scenario. This is, in our opinion, an interesting general research direction, combining logic and game theory in the study of rational information exchange. In this article we take some first steps in this direction: we consider the case where available actions are public announcements, and where each agent has a (typically epistemic) goal formula that she would like to become true. What will each agent announce? The truth of the goal formula also depends on the announcements made by other agents. We analyse such public announcement games.
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This work started life as a presentation at a Workshop on Reasoning about Knowledge and Rational Action in honour of Professor Wiebe van der Hoek on his 50th birthday, Liverpool, UK. A later version was presented at the 6th conference on Logic, Game Theory and Social Choice (LGS 6), Tsukuba, Japan. We thank the anonymous reviewers, as well as attendants at the mentioned meetings, for comments that have helped us improve the paper. We also thank Giacomo Bonanno, Pål Grønås Drange and Stefan Minica for helpful remarks.
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Ågotnes, T., van Ditmarsch, H. What will they say?—Public Announcement Games. Synthese 179 (Suppl 1), 57–85 (2011). https://doi.org/10.1007/s11229-010-9838-8
- Modal logic
- Epistemic logic
- Imperfect information games
- Action logic
- Public announcements