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Epistemic Game Theory without Types Structures: An Application to Psychological Games

Pierpaolo Battigalli (), Roberto Corrao and Federico Sanna

No 641, Working Papers from IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University

Abstract: We consider multi-stage games with incomplete information and observable actions, and we analyze strategic reasoning by means of epistemic events within a "total" state space made of all the profiles of behaviors (paths of play) and possibly incoherent infinite hierarchies of conditional beliefs. Thus, we do not rely on types structures, or similar epistemic models. Subjective rationality is defined by the conjunction of coherence of belief hierarchies, rational planning, and consistency between plan and on-path behavior. Since consistent hierarchies uniquely induce beliefs about behavior and belief hierarchies of others, we can define rationality and common strong belief in rationality, and analyze their behavioral and low-order beliefs implications, which are characterized by strong rationalizability. Our approach allows to extend known techniques to the epistemic analysis of psychological games where the utilities of outcomes depend on beliefs of order k or lower. This covers almost all applications of psychological game theory. JEL Classification Numbers: C72, C73, D82. Keywords: Epistemic game theory, hierarchies of beliefs, consistency, subjective rationality, strong rationalizability, psychological games.

Date: 2019
New Economics Papers: this item is included in nep-gth, nep-hpe, nep-mic and nep-upt
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