A Modal Logic of Epistemic Games
We propose some variants of a multi-modal of joint action, preference and knowledge that support reasoning about epistemic games in strategic form. The first part of the paper deals with games with complete information. We first provide syntactic proofs of some well-known theorems in the area of interactive epistemology that specify some sufficient epistemic conditions of equilibrium notions such as Nash equilibrium and Iterated Deletion of Strictly Dominated Strategies (IDSDS). Then, we present a variant of the logic extended with dynamic operators of Dynamic Epistemic Logic (DEL). We show that it allows to express the notion IDSDS in a more compact way. The second part of the paper deals with games with weaker forms of complete information. We first discuss several assumptions on different aspects of perfect information about the game structure (e.g., the assumption that a player has perfect knowledge about the playersâ€™ strategy sets or about the preference orderings over strategy profiles), and show that every assumption is expressed by a corresponding logical axiom of our logic. Then we provide a proof of Harsanyiâ€™s claim that all uncertainty about the structure of a game can be reduced to uncertainty about payoffs. Sound and complete axiomatizations of the logics are given, as well as some complexity results for the satisfiability problem.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Giacomo Bonanno & Pierpaolo Battigalli, 2003.
"Recent Results On Belief, Knowledge And The Epistemic Foundations Of Game Theory,"
9814, University of California, Davis, Department of Economics.
- Battigalli, Pierpaolo & Bonanno, Giacomo, 1999. "Recent results on belief, knowledge and the epistemic foundations of game theory," Research in Economics, Elsevier, vol. 53(2), pages 149-225, June.
- Pierpaolo Battigali & Giacomo Bonanno, . "Recent Results On Belief, Knowledge And The Epistemic Foundations Of Game Theory," Department of Economics 98-14, California Davis - Department of Economics.
- Adam Brandenburger, 1992. "Knowledge and Equilibrium in Games," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 83-101, Fall.
- Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 263-300.
When requesting a correction, please mention this item's handle: RePEc:gam:jgames:v:1:y:2010:i:4:p:478-526:d:10053. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (XML Conversion Team)
If references are entirely missing, you can add them using this form.