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Rationalizability, Observability and Common Knowledge

Antonio Penta () and Peio Zuazo-Garin

No 1106, Working Papers from Barcelona Graduate School of Economics

Abstract: We study the strategic impact of players' higher order uncertainty over the observability of actions in general two-player games. More specifically, we consider the space of all belief hierarchies generated by the uncertainty over whether the game will be played as a static game or with perfect information. Over this space, we characterize the correspondence of a solution concept which represents the behavioral implications of Rationality and Common Belief in Rationality (RCBR), where `rationality' is understood as sequential whenever a player moves second. We show that such a correspondence is generically single-valued, and that its structure supports a robust refinement of rationalizability, which often has very sharp implications. For instance: (i) in a class of games which includes both zero-sum games with a pure equilibrium and coordination games with a unique efficient equilibrium, RCBR generically ensures efficient equilibrium outcomes; (ii) in a class of games which also includes other well-known families of coordination games, RCBR generically selects components of the Stackelberg pro les; (iii) if common knowledge is maintained that player 2's action is not observable (e.g., because 1 is commonly known to move earlier, etc.), in a class of games which includes of all the above RCBR generically selects the equilibrium of the static game most favorable to player 1.

Keywords: eductive coordination; extensive form uncertainty; first-mover advantage; Krpes hypothesis; higher order beliefs; Rationalizability; robustness; Stackelberg selections (search for similar items in EconPapers)
JEL-codes: C70 C71 C72 D82 D83 (search for similar items in EconPapers)
Date: 2019-07
New Economics Papers: this item is included in nep-gth, nep-hpe and nep-mic
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Working Paper: Rationalizability, observability and common knowledge (2019)
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