Admissibility in Games

Abstract

Suppose that each player in a game is rational, each player thinks the other players are rational, and so on. Also, suppose that rationality is taken to incorporate an admissibility requirement-that is, the avoidance of weakly dominated strategies. Which strategies can be played? We provide an epistemic framework in which to address this question. Specifically, we formulate conditions of rationality and mth-order assumption of rationality (RmAR) and rationality and common assumption of rationality (RCAR). We show that (i) RCAR is characterized by a solution concept we call a "self-admissible set"; (ii) in a "complete" type structure, RmAR is characterized by the set of strategies that survive m + 1 rounds of elimination of inadmissible strategies; (iii) under certain conditions, RCAR is impossible in a complete structure.

Prudent Rationalizability in Generalized Extensive-Form Games

“…PR is equivalent to iterated admissibility on the tree as defined by Brandenburger and Friedenberg (2007). Iterated admissibility on the tree is analogous to iterated dominance conditional on normal-form information setsà la Shimoji and Watson (1994), in which strict dominance is replaced by weak dominance.…”

“…Iterated admissibility on the tree is analogous to iterated dominance conditional on normal-form information setsà la Shimoji and Watson (1994), in which strict dominance is replaced by weak dominance. Brandenburger and Friedenberg (2007) show that iterated admissibility on the tree is equivalent to IA of the strategic form of the game. IA does not require conditioning on normal-form information sets.…”

Logical omniscience at the laboratory

“…Without controlling for beliefs about the rationality and logical omniscience of others, failure to play the equilibrium cannot be interpreted as limited ability to perform iterated reasoning. 9 Consequently, a researcher interested in the ability of humans to perform chains 6 A similar observation is made in Weber (2003). 7 We refer the reader to chapter 5 of Camerer (2003) for a survey of this literature.…”

“…7 We refer the reader to chapter 5 of Camerer (2003) for a survey of this literature. 8 Note that the solution concept of iterated deletion of weakly dominated strategies requires more stringent conditions than common knowledge of rationality (see Brandenburger et al (2008)). 9 The same is true for beauty contests where a logically omniscient player chooses the number corre-4 of iterative reasoning might underestimate the actual ability of humans when relying on choices in beauty contest or centipede games alone.…”

“…Introspection alone was sufficient for subjects to perform better when playing the same puzzles for a second time. 6 Our econometric analysis is organized around these two themes (Section 4). In these studies, the ability of individuals to perform iterative reasoning is associated with their ability to iteratively delete dominated strategies.…”