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2016 | OriginalPaper | Chapter

19. Revealed Attention

Authors : Yusufcan Masatlioglu, Daisuke Nakajima, Erkut Y. Ozbay

Published in: Behavioral Economics of Preferences, Choices, and Happiness

Publisher: Springer Japan

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Abstract

The standard revealed preference argument relies on an implicit assumption that a decision maker considers all feasible alternatives. However, the marketing and psychology literatures provide well-established evidence that consumers do not consider all brands in a given market before making a purchase (Limited Attention). In this chapter, we illustrate how one can deduce both the decision maker’s preference and the alternatives to which she pays attention and inattention from the observed behavior. We illustrate how seemingly compelling welfare judgements without specifying the underlying choice procedure are misleading. Further, we provide a choice theoretical foundation for maximizing a single preference relation under limited attention.

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Varian (2006) provides a nice survey of revealed preference analysis.

As argued in Aumann (2005), this behavior is still considered rational (at least boundedly rational) since she is choosing the best alternative under her limited information about what is available.

Lavidge and Steiner (1961) presented awareness of an item as a necessary condition to be in the consideration set. How unawareness alters the behavior of the DM has been studied in various contexts such as game theory (Heifetz et al., 2010, Dynamic unawareness and rationalizable behavior, unpublished; Ozbay, 2008, Unawareness and strategic announcements in games with uncertainty, unpublished), and contract theory (Filiz-Ozbay, 2010, Incorporating awareness into contract theory, unpublished).

In addition, in financial economics it is shown that investors reach a decision within their limited attention (Huberman and Regev 2001). Similar examples can be found in job search (Richards et al. 1975), university choice (Dawes and Brown 2005), and airport choice (Basar and Bhat 2004).

Without any structure on the formation of the consideration sets, any choice behavior can be rationalized by any preference (Hausman 2008).

See Ambrus and Rozen (2010, Rationalizing choice with multi-self models, unpublished), Apesteguia and Ballester (2010, A measure of rationality and welfare, unpublished), Cherepanov et al. (2010, Rationalization, unpublished), Chambers and Hayashi (2008), Green and Hojman (2008), Manzini and Mariotti (2012), Masatlioglu and Nakajima (2009, Choice by iterative search, unpublished), Noor (2011), and Rubinstein and Salant (2009).

Indeed, Bernheim and Rangel (2007) mention that if we know the DM believes that she is choosing from a set that is other than the objective feasible set, we should take it into account for the welfare analysis (Section III B).

While this paper is complementary to our paper, their implications are completely different We discuss it in the Conclusion section.

Throughout the paper, unless it leads to confusion, we abuse the notation by suppressing set delimiters, e.g. writing c(xy) instead of c({x, y}) or Γ(xy) instead of Γ({x, y}) or S∖x instead of S∖{x}.

The only exception is that the feasible set itself conveys some information that affects her belief or cost function.

Salant and Rubinstein (2008) characterizes this class of choice functions by assuming N is observable.

This heuristic is very close to “Rationalization” of Cherepanov et al. (2010, Rationalization, unpublished). Indeed, it is a special version of Rationalization. In their model, unlike “the top on each criterion”, depending on the feasible set, different sets of criteria might be utilized to eliminate alternatives in the first stage. See Sect. 4 for further discussion.

For instance, suppose store A deals with Makers 1 and 2’s bikes while store B sells bikes from Makers 2 and 3. Then, the DM compares the number of Makers 1 and 2’s bikes with that of Makers 2 and 3’s to choose which store to visit.

That is, c(S) ∈ Γ(S) and $c(S) \succ x$ for all $x \in \varGamma (S)\setminus c(S)$.

In the extreme case where the choice data satisfy the weak axiom of revealed preference, we have no way of knowing whether the decision maker is aware of all alternatives and maximizing a particular preference, or whether she only pays attention to the one she chooses. In the latter, her preference has no significant importance. In Sect. 6, we discuss the situations where one can pin down the preference even in this extreme case.

For a detailed discussion of this subject, see Manzini and Mariotti (2009, Choice based welfare economics for boundedly rational agents, unpublished).

“The top on each criterion” introduced in Sect. 2.1 coincides with the rationalization model when all rationales are complete.

Actually, Manzini and Mariotti (2007) do not require the second rationale (P ₂) to be complete and transitive (it only requires P ₂ to be asymmetric). We put the stronger requirement on P ₂ in order to highlight that the difference between these models is generated by the first stage, not by the incompleteness or intransitivity of the second rationale, which corresponds to the DM’s preference in our model.

One can show that if P ₁ is transitive, the first stage elimination generates an attention filter so the resulting choice will be a CLA as long as P ₂ is complete and transitive.

This phenomenon is well-documented and robust in behavioral research on marketing (Huber et al. 1982; Tversky and Simonson 1993), including choices among monetary gambles, political candidates, job candidates, environmental issues, and medical decision making. Advertising irrelevant alternatives is commonly used as a marketing strategy to invoke the attraction effect on the customers.

The standard continuity is inconsistent with the attraction effect: x = c(x, d _n, y) for all n but y is chosen at the limit (y = c(x, y)) where {d _n} is a sequence of x’s decoys converging to x. Nevertheless, the model can still enjoy a weaker continuity along with the attraction effect. For example, assume $y_{n} \rightarrow y$ and $y,y_{n}\not\in S,$ then

$$\displaystyle{ \mbox{ If }y_{n}\not\in c(S \cup y_{n})\mbox{ then }\{y\}\neq c(S \cup y_{n}). }$$

Indeed, one can show that the CLA is continuous in this sense if $\succ $ is continuous and the attention filter satisfies: (a) $y_{n}\not\in \varGamma (S \cup y_{n})$ implies $y\not\in \varGamma (S \cup y)$ and (b) $z \in \varGamma (S \cup y_{n})$ implies $z \in \varGamma (S \cup y)$ when $y_{n} \rightarrow y$.

Eliaz and Spiegler (2011) studied a game theoretical model where firms would like to influence consumers’ consideration sets by introducing costly decoys.

This generalized attraction effect is another example that lies outside of recent models provided in Cherepanov et al. 2008, Manzini and Mariotti (2012) and Lleras et al. (2010, When more is less: choice by limited consideration, unpublished) since it does not satisfy Weak-WARP. There are two exceptions: Ok et al. (2010, Revealed (p)reference theory, unpublished) and de Clippel and Eliaz (2012). However, these two models can accommodate neither Cyclical nor Choosing Pairwisely choice patterns.

In this regard, our theory highlights the importance of other tools (besides observed choice) which can shed light on the choice process rather than outcome.

This order is not necessarily complete, as in this example; Michigan does not compare its students with candidates from other schools.

This addendum has been newly written by Daisuke Nakajima for this book chapter.

Nakajima appreciates the financial support provided by Japan Society for the Promotion of Science (JSPS KAKENHI Grant Number 26780113).

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Title: Revealed Attention
Authors: Yusufcan Masatlioglu
Daisuke Nakajima
Erkut Y. Ozbay
Publisher: Springer Japan
Book: Behavioral Economics of Preferences, Choices, and Happiness
Print ISBN: 978-4-431-55401-1

Electronic ISBN: 978-4-431-55402-8

Copyright Year: 2016
DOI: https://doi.org/10.1007/978-4-431-55402-8_19