Misperception and Cognition in Markets
Abstract
:1. Introduction
2. Related Literature
3. The Model
3.1. Formal Details
 (i)
 ${\sigma}_{k}^{*}(\mathbf{X})(x)>0$ only if $x\in arg\underset{\tilde{x}\in \mathbf{X}}{max}{V}_{k}(\tilde{x})$ for $k\in \{S,N\}$; and
 (ii)
 ${\alpha}^{*}(\mathbf{X})({a}^{\prime})>0$ only if ${a}^{\prime}\in arg\underset{a\in \{S,N\}}{max}\mathcal{V}(a\mathbf{X})$,
3.2. Efficient and Exploitative Good Provision
3.3. Discussion of Key Modeling Assumptions
4. Results
4.1. Exogenous Cognitive States
 (a)
 the efficient product ${x}_{S}^{m}\equiv (h(\theta ),\theta h(\theta ))$ if sophisticated; and
 (b)
 the inefficient product ${x}_{N}^{m}\equiv (h(\theta +\Delta ),(\theta +\Delta )h(\theta +\Delta ))$ if naive.
 (a)
 the efficient product ${x}_{S}^{c}\equiv (h(\theta ),C(h(\theta ))$ if sophisticated; and
 (b)
 the inefficient product ${x}_{N}^{c}\equiv (h(\theta +\Delta ),C(h(\theta +\Delta )))$ if naive.
 (a)
 total surplus under monopoly and competition coincide; and
 (b)
 consumer surplus is strictly higher under competition relative to monopoly.
4.2. Cognitive Equilibrium
4.2.1. Monopoly
4.2.2. Competition
 (a)
 invests in cognition and selects ${x}_{S}^{c}$ for $\kappa \le {\overline{\kappa}}^{c}$; and
 (b)
 does not invest in cognition and selects ${x}_{N}^{c}$ for $\kappa >{\overline{\kappa}}^{c}$.
4.2.3. Comparing Monopoly to Competition
 (a)
 monopoly is more efficient; and
 (b)
 consumer surplus is higher under competition.
5. Conclusions and Discussion
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
Notes
1  Naiveté has been used to explain why people procrastinate [1,2,3], overestimate future gym attendance [4,5], struggle to avoid hidden addons or fees [6], and deviate from their selfset goals [7]. It has also been used to explain marketbased phenomena. For example, DellaVigna and Malmendier use naiveté to explain the prevalence of signup bonuses coupled with above marginal cost pricing for leisure goods (such as credit cards) and the prevalence of high signup costs with lowerthan marginal cost pricing for investment activities (such as attending a health club) [8]. 
2  For example, all the papers cited in Footnote 1 make this assumption. 
3  For example, in their influential book “Thinking Fast and Slow”, Kahneman describes a dualsystem of decisionmaking in which System 1 is a fast, intuitive thinker potentially prone to bias and System 2 is a slow, contemplative thinker that effectively optimizes [9]. He argues that, most of the time, System 1 is in control of our decisions but System 2 will take over when the situation is warranted. 
4  This will be useful notation for describing equilibrium provision of the good to the consumer. 
5  Since each ${X}_{i}$ is finite, $\mathbf{X}$ is also finite. As a result, the consumer will always be able to make an optimal choice from $\mathbf{X}$. 
6  For example, the product $x=(h(\theta ),\theta h(\theta ))$ is such that ${V}_{N}(x)=\Delta h(\theta )>0$. 
7  Indeed, the utility of a naive consumer from product $(h(\theta ),\theta h(\theta ))$ is
$${V}_{N}((h(\theta ),\theta h(\theta ))=(\theta +\Delta )h(\theta )\theta h(\theta )=\Delta h(\theta )>0.$$

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Young, B. Misperception and Cognition in Markets. Games 2022, 13, 71. https://doi.org/10.3390/g13060071
Young B. Misperception and Cognition in Markets. Games. 2022; 13(6):71. https://doi.org/10.3390/g13060071
Chicago/Turabian StyleYoung, Benjamin. 2022. "Misperception and Cognition in Markets" Games 13, no. 6: 71. https://doi.org/10.3390/g13060071