Savage vs. Anscombe-Aumann: an experimental investigation of ambiguity frameworks
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Savage vs. Anscombe-Aumann: an experimental investigation of ambiguity frameworks Jo¨rg Oechssler1,3 • Alex Roomets2 Accepted: 21 September 2020 Ó The Author(s) 2020
Abstract The Savage and the Anscombe–Aumann frameworks are the two most popular approaches used when modeling ambiguity. The former is more flexible, but the latter is often preferred for its simplicity. We conduct an experiment where subjects place bets on the joint outcome of an ambiguous urn and a fair coin. We document that more than a third of our subjects make choices that are incompatible with Anscombe–Aumann for any preferences, while the Savage framework is flexible enough to account for subjects’ behaviors. Keywords Ellsberg paradox Ambiguity Experiment
We would like to thank Adam Dominiak, Peter Du¨rsch, Ju¨rgen Eichberger, Jean-Philippe Lefort, two anonymous referees, and participants of the conference on Ambiguity and Strategic Interactions in Grenoble in honor of Ju¨rgen Eichberger for comments. Franklin and Marshall College provided financial support for the experiments. Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11238020-09778-w) contains supplementary material, which is available to authorized users. & Jo¨rg Oechssler [email protected] Alex Roomets [email protected] 1
University of Heidelberg, Heidelberg, Germany
2
Franklin and Marshall College, Lancaster, Pennsylvania, USA
3
Department of Economics, University of Heidelberg, Bergheimer Str. 58, 69115 Heidelberg, Germany
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J. Oechssler, A. Roomets
1 Introduction The Savage (1954) and the Anscombe and Aumann (1963) frameworks are the two most popular approaches when it comes to modeling ambiguity. The latter is a twostage model where acts are maps from states to objective lotteries over consequences. It is often preferred for its simplicity, but the Savage model provides more flexibility. Gilboa and Schmeidler (1989) and Schmeidler (1989) used the Anscombe and Aumann approach as a basis for their seminal contributions to ambiguity theory. Eichberger and Kelsey (1996) show that, for standard ambiguity models like Choquet-expected utility (CEU) and Maxmin Expected Utility, ambiguity aversion implies a strict preference for randomization when looked at in the Anscombe–Aumann framework. They also show that the same need not hold in the Savage framework. Eichberger and Kelsey (1996) argue against the plausibility of a general preference for randomization but also admit the need for further experiments on this question.1 We implement an experiment in which some choices are inconsistent with ambiguity models that are based on the preference framework of Anscombe and Aumann (1963). We show that these choices can be consistent within a Savage framework using, e.g., a CEU model as in Eichberger and Kelsey (1996). The experiment involves subjects choosing from among six options that each relates to the outcomes of a coin flip and a draw from an ambiguous, 2-color urn. Two of the six
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