A model of state aggregation
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A model of state aggregation Anastasia Burkovskaya1 Received: 7 December 2019 / Accepted: 23 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this paper, due to limited attention and lack of focus, an agent has tendency toward framing of available information that drives her to see the state space as a collection of the events or “small worlds” related to a particular ambience, which we call a state aggregation. This work axiomatizes the model of state aggregation, shows how to recover the structure of the “small worlds” together with beliefs and utility from the individual demand for assets, and provides comparative statics and revealed preference restrictions. Keywords Limited attention · Lack of focus · Framing · Identification · State aggregation JEL Classification D11 · D81
1 Introduction With mounting evidence from the psychology literature, the belief that the framing of a decision problem affects individual decision-making has gained an ever-growing acceptance in economics.1 This paper captures the framing effect in economic decision-making that arises from limited attention and lack of focus by introducing the notion of state aggregation to the otherwise standard subjective expected utility (SEU) theory of Savage (1954). It also obtains identification results for how framing occurs and Afriat-style rationalizability restrictions on a finite dataset. The idea of state aggregation is inspired by Savage’s thoughts on the applicability of Bayesian methods to real-world problems. Although an uncountable set of states Ω is often assumed for SEU representation, “a smaller world is derived from (this) larger world by neglecting some distinctions between states, not by ignoring some set 1 e.g., Salant and Rubinstein (2008), Eliaz and Spiegler (2011), Piccione and Spiegler (2012), Dreber et al.
(2013), Bordalo et al. (2016), Salant and Siegel (2018).
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Anastasia Burkovskaya [email protected] Office 638 Social Sciences Building A02, University of Sydney, Sydney, NSW 2006, Australia
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of states outright.” Thus, the decision-maker views the world in terms of a partition, say, π , of Ω. A partition, derived from the preferences, captures the idea of a frame in our paper. In this paper, the sure-thing principle applies only to events measurable with respect to π , which gives us an analogue of classical SEU—the state aggregation subjective expected utility (SASEU) (our Theorem 1). SASEU representation is akin to a two-stage process in which the agent first calculates the expected utility for each event A in π as usual using a standard vNM utility function, say, v, and then computes the expected utility across various events in π using another possibly vNM utility function φ to evaluate the utility in each A. Analogously to attitudes to risk, we may now ask a similar question about changes in behavior with respect to changes in the state aggregation π . The curvature of φ enables us to measure these responses. We say the agent is event-ri
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