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Epistemic logic meets epistemic game theory: a comparison between multi-agent Kripke models and type spaces

Galeazzi, Paolo and Lorini, Emiliano Epistemic logic meets epistemic game theory: a comparison between multi-agent Kripke models and type spaces. (2016) Synthese, 193 (7). 2097-2127. ISSN 0039-7857

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Official URL: https://doi.org/10.1007/s11229-015-0834-x

Abstract

In the literature there are at least two main formal structures to deal with situations of interactive epistemology: Kripke models and type spaces. As shown in many papers (see Aumann and Brandenburger in Econometrica 36:1161–1180, 1995; Baltag et al. in Synthese 169:301–333, 2009; Battigalli and Bonanno in Res Econ 53(2):149–225, 1999; Battigalli and Siniscalchi in J Econ Theory 106:356–391, 2002; Klein and Pacuit in Stud Log 102:297–319, 2014; Lorini in J Philos Log 42(6):863–904, 2013), both these frameworks can be used to express epistemic conditions for solution concepts in game theory. The main result of this paper is a formal comparison between the two and a statement of semantic equivalence with respect to two different logical systems: a doxastic logic for belief and an epistemic–doxastic logic for belief and knowledge. Moreover, a sound and complete axiomatization of these logics with respect to the two equivalent Kripke semantics and type spaces semantics is provided. Finally, a probabilistic extension of the result is also presented. A further result of the paper is a study of the relationship between the epistemic–doxastic logic for belief and knowledge and the logic STIT (the logic of “seeing to it that”) by Belnap and colleagues (Facing the future: agents and choices in our indeterminist world, 2001).

Item Type:Article
Additional Information:Thanks to Springer editor. The original PDF can be found at Synthese (ISSN 0039-7857) website : https://link.springer.com/article/10.1007/s11229-015-0834-x
HAL Id:hal-01809280
Audience (journal):International peer-reviewed journal
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Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Other partners > University of Amsterdam - UvA (NETHERLANDS)
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Deposited By: IRIT IRIT
Deposited On:02 May 2018 14:14

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