A framework for robustness to ambiguity of higher-order beliefs

Stauber, Ronald

doi:10.1007/s00182-013-0394-6

“…Within a standard Bayesian decision-theoretic model, Barelli and Galanis (2013) provide a characterization for iterated admissibility by introducing an exogenous 'tie breaking' criterion. Robustness to ambiguity is studied by Stauber (2011Stauber ( , 2014 with a different interpretation than ours.…”

Section: Introductionmentioning

confidence: 95%

Strategic cautiousness as an expression of robustness to ambiguity

Ziegler

¹

,

Zuazo-Garin

²

2020

Games and Economic Behavior

3

0

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Economic predictions often hinge on two intuitive premises: agents rule out the possibility of others choosing unreasonable strategies ('strategic reasoning'), and prefer strategies that hedge against unexpected behavior ('cautiousness'). These two premises conflict and this undermines the compatibility of usual economic predictions with reasoning-based foundations. This paper proposes a new take on this classical tension by interpreting cautiousness as robustness to ambiguity. We formalize this via a model of incomplete preferences, where (i) each player's strategic uncertainty is represented by a possibly non-singleton set of beliefs and (ii) a rational player chooses a strategy that is a best-reply to every belief in this set. We show that the interplay between these two features precludes the conflict between strategic reasoning and cautiousness and therefore solves the inclusion-exclusion problem raised by Samuelson (1992). Notably, our approach provides a simple foundation for the iterated elimination of weakly dominated strategies.

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Trembles in extensive games with ambiguity averse players

Aryal

¹

,

Stauber

²

2014

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We introduce and analyze three definitions of equilibrium for finite extensive games with imperfect information and ambiguity averse players. In a setting where players' preferences are represented by maxmin expected utility as characterized in Gilboa and Schmeidler (1989), our definitions capture the intuition that players may consider the possibility of slight mistakes, analogous to the intuition leading to trembling-hand perfect equilibrium as introduced in Selten (1975). We prove existence for two of our equilibrium notions, and relate our definitions to standard equilibrium concepts with expected utility maximizing players. Our analysis shows that ambiguity aversion can lead to distinct behavioral implications, even if ambiguous beliefs only arise from the possibility of slight mistakes in the implementation of unambiguous strategies.

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Trembles in Extensive Games with Ambiguity Averse Players

Aryal

¹

,

Stauber

²

2013

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We introduce and analyze three definitions of equilibrium for finite extensive games with imperfect information and ambiguity averse players. In a setting where players' preferences are represented by maxmin expected utility as characterized in Gilboa and Schmeidler (1989), our definitions capture the intuition that players may consider the possibility of slight mistakes, analogous to the intuition leading to trembling-hand perfect equilibrium as introduced in Selten (1975). We prove existence for two of our equilibrium notions, and relate our definitions to standard equilibrium concepts with expected utility maximizing players. Our analysis shows that ambiguity aversion can lead to distinct behavioral implications, even if ambiguous beliefs only arise from the possibility of slight mistakes in the implementation of unambiguous strategies.

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A framework for robustness to ambiguity of higher-order beliefs

Cited by 4 publications

References 32 publications

Strategic cautiousness as an expression of robustness to ambiguity

Strategic cautiousness as an expression of robustness to ambiguity

Trembles in extensive games with ambiguity averse players

Trembles in Extensive Games with Ambiguity Averse Players

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