Pathwise Concentration Bounds for Misspecified Bayesian Beliefs

Fudenberg, Drew; Lanzani, Giacomo; Strack, Philipp

doi:10.2139/ssrn.3805083

Cited by 5 publications

(4 citation statements)

References 43 publications

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“…Fudenberg, Lanzani, and Strack (2021a) showed that a limit action must be a best reply to all of the associated KL minimizers when the prior has subexponential decay. An earlier version of this paper, Fudenberg, Lanzani, and Strack (2022), use the results here to give a simpler and more transparent proof of this result.…”

Section: The Importance Of Pathwise Concentrationmentioning

confidence: 84%

Pathwise concentration bounds for Bayesian beliefs

Fudenberg,

Lanzani,

Strack

2023

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We show that Bayesian posteriors concentrate on the outcome distributions that approximately minimize the Kullback–Leibler divergence from the empirical distribution, uniformly over sample paths, even when the prior does not have full support. This generalizes Diaconis and Freedman's (1990) uniform convergence result to, e.g., priors that have finite support, are constrained by independence assumptions, or have a parametric form that cannot match some probability distributions. The concentration result lets us provide a rate of convergence for Berk's (1966) result on the limiting behavior of posterior beliefs when the prior is misspecified. We provide a bound on approximation errors in “anticipated‐utility” models, and extend our analysis to outcomes that are perceived to follow a Markov process.

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Section: The Importance Of Pathwise Concentrationmentioning

confidence: 84%

Pathwise concentration bounds for Bayesian beliefs

Fudenberg,

Lanzani,

Strack

2023

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“…As in previous work, we have assumed that agents have non-doctrinaire priors in order to appeal to the Diaconis and Freedman (1990) result on the speed of convergence of Bayesian posteriors to the empirical distribution. Fudenberg, Lanzani, and Strack (2021) extends their convergence result to priors without full support, but if the true state is outside of the support of the priors then agents need not stop experimenting in finite time, as shown by Fudenberg, Romanyuk, and Strack (2017). This raises a suite of new issues, as patiently stable states might not be Nash equilibria.…”

Section: Discussionmentioning

confidence: 99%

“…This follows from the Fudenberg, Lanzani, and Strack (2021) extension of the pathwise concentration result of Diaconis and Freedman (1990) to priors that do not have full support. The support restriction arise because the agent's prior is concentrated on distributions that can be generated by independent randomizations of their opponents.…”

Section: A5 Proof Of Propositionmentioning

confidence: 97%

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Observability, Dominance, and Induction in Learning Models

Clark,

Fudenberg,

2022

Preprint

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Learning models do not in general imply that weakly dominated strategies are irrelevant or justify the related concept of "forward induction," because rational agents may use dominated strategies as experiments to learn how opponents play, and may not have enough data to rule out a strategy that opponents never use. Learning models also do not support the idea that the selected equilibria should only depend on a game's normal form, even though two games with the same normal form present players with the same decision problems given fixed beliefs about how others play. However, playing the extensive form of a game is equivalent to playing the normal form augmented with the appropriate terminal node partitions so that two games are information equivalent, i.e., the players receive the same feedback about others' strategies.

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Observability, dominance, and induction in learning models

Clark

Fudenberg²,

2022

Journal of Economic Theory

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Pathwise Concentration Bounds for Misspecified Bayesian Beliefs

Cited by 5 publications

References 43 publications

Pathwise concentration bounds for Bayesian beliefs

Pathwise concentration bounds for Bayesian beliefs

Observability, Dominance, and Induction in Learning Models

Observability, dominance, and induction in learning models

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