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In the latest issue of Econometrica, one of the TOP 5 journals in May 2020 The figure of Bytedance appeared on it.
The authors are Shaowei Ke, Assistant Professor at the University of Michigan and Qi Zhang, ByteDance Technology.
"Randomization and Fuzzy Aversion"
Abstract: Randomization/hybrid strategies are common, but how to model ambiguity (some maxmin principles) is unclear. We prove that the individual’s belief in how the unknown law of probability is determined is important for understanding this problem. We adopted the framework of Anscombe and Aumann (1963) and relaxed the axioms. In the final representation of individual preferences, the individual has a set of prior values M. She believes that nature has selected an unknown scene (a set of prior values) from M before it moves. From this scene, nature will choose a prior value after she moves. This representation illustrates how randomization can partially eliminate the effects of blur.
Brief introduction
In economics, people often assume that a person has a unique subjective prior (probability measure) for countries in the world, even if the true law of probability (if it has been determined) is rarely provided. Ellsberg (1961) introduced an intuitive thinking experiment to prove that, on the contrary, an individual usually faces a vague state and is a vague aversion; that is to say, she does not have a unique a priori, and does not like to respond without a unique subjective probability assessment. Event betting. In an experiment, assuming that a correct bet produces $100 and a wrong bet produces $0, it is predicted to face a risky urn (an urn containing 50 red and 50 black balls) and an ambiguous urn ( A person with 100 red and black balls, but the ratio is unknown), would prefer to bet on the color of balls drawn randomly from risky urns rather than on ambiguous urns. Nevertheless, if any urn is fixed, the individual will show no difference in any color of the randomly drawn ball. This prediction has been confirmed by many follow-up studies.
In a seminal paper, Gilboa and Schmeidler (1989) introduced the Maxmin Expected Utility (MEU) model to capture fuzzy aversion. In the model, individuals have multiple priorities. In order to evaluate an alternative, such as a bet, she uses a priori that minimizes its utility; in order to select from multiple alternatives, she maximizes the minimal utility. This explanation is that, considering multiple priors, the individual is conservative and focuses on the worst-case scenario-or equivalently, the individual believes that it is natural to choose the worst probability law from a set of fixed laws, and thus It's not good for her.
The MEU model, or more broadly, the maxmin principle, is useful in all fields of economics, including contract theory, mechanism design, macroeconomics, finance, etc. However, it is surprising how in these applications, a basic concept in economics "randomization/mixed strategy" should be modeled when individual behavior conforms to the MEU model or any other maxmin criteria. Randomization is modeled differently in different applications, or simply eliminated; sometimes the difficulty of randomization and various randomization modeling methods are discussed, but there is no general principle that can help us better understand how randomization should be Modeling in which way and in which application.
In this article, we introduced a fuzzy random theory, which may help solve this problem. We are concerned about randomization under the MEU model, but our findings can be applied to other fuzzy models and other maxmin criterion models.
English summary:
We propose a model of preferences in which the effect of randomization on ambiguity depends on how the unknown probability law is determined. We adopt the framework of Anscombe and Aumann (1963) and relax the axioms. In the resulting representation of the individual's preference, the individual has a collection of sets of priors . She believes that before she moves, nature has chosen an unknown scenario (a set of priors) from , and from that scenario, nature will choose a prior after she moves. The representation illustrates how randomization may partially eliminate the effect of ambiguity.
原文下载链接：https://www.econometricsociety.org/publications/econometrica/2020/05/01/randomization-and-ambiguity-aversion
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