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An epistemic analysis of dynamic games with unawareness. (English) Zbl 1437.91085

Summary: We introduce a novel framework to describe dynamic interactive reasoning in presence of unawareness. We extend the notion of conditional probability systems for this setting and we perform the construction of the corresponding canonical hierarchical structure, that is, the structure that contains all coherent infinite hierarchies of beliefs in presence of unawareness and conditioning events, which is an extension of the one constructed in [P. Battigalli and M. Siniscalchi, J. Econ. Theory 88, No. 1, 188–230 (1999; Zbl 0972.91020)]. Relying on the existence of this object, we provide an epistemic characterization of strong rationalizability of D. G. Pearce [Econometrica 52, 1029–1050 (1984; Zbl 0552.90097)] as defined in [A. Heifetz et al., Games Econ. Behav. 81, 50–68 (2013; Zbl 1281.91020)] to address the case of dynamic games with unawareness. The characterization is based on the notion of strong belief, introduced in the literature by P. Battigalli and M. Siniscalchi [J. Econ. Theory 106, No. 2, 356–391 (2002; Zbl 1038.91013)].

MSC:

91A25 Dynamic games
91A26 Rationality and learning in game theory
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