Hierarchies of Beliefs and Common Knowledge

By Adam Brandenburger, Eddie Dekel. 1993

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Citations in the corpus

Multi-Agent Cooperation and the Emergence of (Natural) Language (2016, background): “Common knowledge, in game-theoretic parlance, are facts that everyone knows, everyone knows that everyone knows, and so on (Brandenburger et al., 2014).”
Foundations of Dominant Strategy Mechanisms (2007, methodology): “By Mertens and Zamir (1985) and Brandenburger and Dekel (1993), there is a homeomorphism between T i and ∆(V−i × T ∗ −i) and thus the latter is compact.”
Uniform Topologies on Types (2010, background): “[445, 446, 447, 448, 450, 453, 454, 459, 460, 462, 463, 469] Dekel, Eddie, Drew Fudenberg, and Stephen Morris (2007), “Interim correlated rationalizability.””
A Framework for Sequential Planning in Multi-Agent Settings (2005, methodology): “(1)Implicit in the definition of nested beliefs is the assumption of coherency [7].”
Rationalizability in infinite, dynamic games with incomplete information (2003, background): “35 The original definition and informal motivation of the IIC can be found in Cho and Kreps (1987). 36 Their analysis is extended to auctions with interdependent (affiliated) valuations.”
Bargaining and the Nature of War (2004, background): “Although to many game theorists, this is a controversial modeling approach, scholars such as Boge and Eisele (1979), Mertens and Zamir (1985), Brandenburger and Dekel (1993), Nyarko (1990, 1997), Morris (1995), and Gul (1998) construct logically consistent information models that allow for both comm”
ADMISSIBILITY IN GAMES (2008, unknown): “(See Blume-Brandenburger-Dekel [13, 1991].)”
On the Generic (Im)possibility of Full Surplus Extraction in Mechanism Design (2006, background): “into which every other type space T can be uniquely mapped in a beliefs-preserving way (Mertens and Zamir, 1985; Brandenburger and Dekel, 1993; and Heifetz, 1993).”
A Structure Theorem for Rationalizability with Application to Robust Predictions of Refinements (2007, background): “Brandenburger and Dekel (1987) have shown that given a distribution on rationalizable strategy profiles of a given complete-information game, we can enrich the type space by adding payoff-irrelevant types and find an equilibrium in the new game that yields the same distribution on the strategy…”
Hierarchies of Belief and Interim Rationalizability (2004, background): “Furthermore, by an extension of the results of Mertens and Zamir (1985) and Brandenburger and Dekel (1987) (our Theorem 1), all∆-hierarchies can be collected into a single, “universal" type space U (∆Ω) over∆Ω.”