Rationally Inattentive Research Articles

Pricing model of ride-hailing platform considering rationally inattentive passengers

ABSTRACT The ride-hailing services are booming in our daily lives, but it is unclear that how the platforms should set prices to maximize their profits when facing one kind of rationally inattentive passengers in a two-sided market. To fill this gap, we establish a profit maximization model for the ride-hailing platform based on queuing theory and rational inattention theory and analyze the properties of the model. Numerical examples are presented to demonstrate the impacts of perceived high and low service levels, information cost and prior belief on the optimal price and commission rate of the ride-hailing platform. The results show that (1) for different cities, there is always an optimal pricing strategy to maximize the profit of the platform. (2) To ensure maximum profit, the platform should disclose the service information of ride-hailing as much as possible, but also maintain the unknownness of ride-hailing services appropriately.

Competing to Commit: Markets with Rational Inattention

Two homogeneous-good firms compete for a consumer’s unitary demand. The consumer is rationally inattentive and pays entropy costs to process information about firms’ offers. Compared to a collusion benchmark, competition produces two effects. As in standard models, competition puts downward pressure on prices. But, additionally, an attention effect arises: the consumer engages in trade more often. This alleviates the commitment problem that firms have when facing inattentive consumers and increases trade efficiency. For high enough attention costs, the attention effect dominates the effect on prices: firms’ profits are higher under competition than under collusion. (JEL D11, D21, D43, D83, L12)

Linear quadratic approximation of rationally inattentive control problems

AbstractThis paper proposes a linear quadratic approximation approach to dynamic nonlinear rationally inattentive control problems with multiple states and multiple controls. An efficient toolbox to implement this approach is provided. Applying this toolbox to five economic examples demonstrates that rational inattention can help explain the comovement puzzle in the macroeconomics literature.

Rational inattention in discrete choice models: Estimable specifications of RI-multinomial logit (RI-MNL) and RI-nested logit (RI-NL) models

As opposed to the fully informed choice-making assumption in classical discrete choice models, the theory of Rational Inattention (RI)11RI is used interchangeably for ‘Rational Inattention’ or ‘Rationally Inattentive’ throughout the paper in discrete choice modelling has been recently proposed in the literature. Matějka and McKay (2015) proposed the RI-multinomial logit (RI-MNL), and Fosgerau et al. (2020) proposed the RI-nested logit (RI-NL) model. These models consider that choice makers are bayesian agents with prior probabilities of choices and process any further information assuming an information processing cost to have the updated/posterior choice probabilities. However, the proposed RI-MNL and RI-NL models are theoretical formulations without any estimable empirical specifications. This paper proposes econometric formulations of RI-MNL and RI-NL models that are estimable using classical maximum likelihood estimation methods and suitable for revealed crossectional choice data. The proposed models are estimated for commuting mode choices in the Greater Toronto and Hamilton Area (GTHA) using data from a household travel survey conducted in the region. Empirical investigation reveals that the induction of RI in the classical discrete choice models (MNL and NL) improves the model fit by large margins. While scale parameterization in classical MNL and NL does not make a better model, the scale parameterization better captures the choice heterogeneity within the RI framework. Between the RI-MNL and RI-NL, the RI-NL is proven to be the best. The RI-NL model can capture asymmetric (between increasing and decreasing values) elasticities of choice attributes.

Unrestricted information acquisition

In many strategic environments, information acquisition is a central component of the game that is played. Being uncertain about a payoff‐relevant state, a player in a game has a twofold incentive to acquire information: learning the state and learning what others know. We develop a model of information acquisition in games that accounts for players' incentive to learn what others know. In applications to rational inattention and global games, we prove the power of this incentive. When information acquisition is “independent,” that is, players can acquire information only about the state, severe coordination problems emerge among rationally inattentive players. When information acquisition is “unrestricted,” that is, players can acquire information about the state and each other's information in a flexible way, we show that rational inattention admits a sharp logit characterization and we provide a new rationale for selecting risk dominant equilibria in coordination games.

Rationally inattentive monetary policy

This paper studies optimal monetary policy under rational inattention: the policy maker optimally chooses her information subject to a processing constraint. Our analytical results emphasize how the policy maker's information choices shape her expectations and the dynamics of the macroeconomy. Paying attention to demand shocks lowers output volatility and causes untracked supply shocks to drive inflation. Because persistent supply shocks have a minor impact on interest rates under full information in the New Keynesian model, the policy maker should bias her limited attention towards demand shocks. Improvements in information can explain a declining slope of the empirical Phillips curve.

Bayesian Games with Rationally Inattentive Players

We study how scarcity of attention affects strategic choice behaviour in a 2-player incomplete information entry game. Scarcity of attention is a common psychological character among population ( Kahnemann, 1973 , Attention and effort, Prentice Hall), and it is modelled by the rational inattention approach introduced by Sims (1998 , Carnegie-Rochester Conference Series on Public Policy, 49, 317–356). In this game, players acquire information about their private payoff shocks at a cost, which follows a high-low binary distribution. We find that high information cost can generate multiple equilibria, and the number of equilibria differs with respect to different ranges of information cost. The number of equilibria could be 1, 5 or 3. Increasing the information cost could encourage or discourage a player to choose entry in some equilibria. This depends on whether the prior probability of high payoff shocks is greater than a given threshold value. We also exhibit a necessary and sufficient condition of parameter specification such that with the same set of parameters satisfying this condition, both the rational inattention Bayesian game and a Bayesian quantal response equilibrium game where the observation errors are additive and follow a Type-I extreme value distribution can have a common equilibrium. JEL: C72, D91

Rationally Inattentive Behavior: Characterizing and Generalizing Shannon Entropy

We provide a full behavioral characterization of the standard Shannon model of rational inattention. The key axiom is Invariance under Compression, which identifies this model as capturing an ideal form of attention-constrained choice. We introduce tractable generalizations that allow for many of the known behavioral violations from this ideal, including asymmetries and complementarities in learning, context effects, and low responsiveness to incentives. We provide an even more general method of recovering attention costs from behavioral data. The data set in which we characterize all behavioral patterns is state dependent stochastic choice data.

Rational inattention, menu costs, and multi-product firms: Micro evidence and aggregate implications

Using a New Zealand firm-level survey, I show that firms producing more goods have both better information about inflation and more frequent but smaller price changes. To explain these empirical findings, I develop a general equilibrium menu cost model with rationally inattentive multi-product firms. I show that the interaction of nominal and informational rigidities leads to a new selection effect: Price adjusters are better informed than non-adjusters. This selection endogenously generates a leptokurtic distribution of desired price changes, which amplifies monetary non-neutrality. Compared to a one-product baseline, the real effects of monetary shocks are 12 percent smaller in a two-product model.

Hamilton–Jacobi–Bellman–Isaacs equation for rational inattention in the long-run management of river environments under uncertainty

A new stochastic control model for the long-run environmental management of rivers is mathematically and numerically analyzed, focusing on a modern sediment replenishment problem with unique nonsmooth and nonlinear properties. Rational inattention as a novel adaptive strategy to collect information and intervene against the target system is modeled using Erlangization. The system dynamics containing the river discharge following a continuous-state branching with an immigration-type process and the controlled sediment storage dynamics lead to a nonsmooth and nonlocal infinitesimal generator. Modeling uncertainty, which is ubiquitous in certain applications, is considered in a robust control framework in which deviations between the benchmark and distorted models are penalized through relative entropy. The partial integro-differential Hamilton–Jacobi–Bellman–Isaacs (HJBI) equation as an optimality equation is derived, and its uniqueness, existence, and optimality are discussed. A monotone finite difference scheme guaranteeing the boundedness and uniqueness of numerical solutions is proposed to discretize the HJBI equation and is verified based on manufactured solutions. Model applications are also conducted with the parameter values identified from the available data and physical formulae. The computational results suggest that environmental management should be rationally inattentive in a state-dependent and adaptive manner.

Beauty Contest with Rationally Inattentive Agents

In the context of a beauty-contest coordination game, players choose how much costly attention to pay to public information. Introducing information costs based on rational inattention implies that, in the neighborhood of zero information costs, multiple equilibria can emerge in settings that without information costs would imply unique linear equilibrium. Agents have a coordination motive arising from strategic complementarity in their actions, which, in turn, implies coordinating on attention devoted to the public signal. This effect induces multiple equilibrium levels of attention at intermediate levels of transparency of public information (worth paying attention to if others do, but not worth paying attention to if others do not) for small enough information costs. Formally, the set of equilibria under rational inattention does not converge to the set of equilibria without information costs as the price of attention approaches zero. Quintessentially, small deviations from rationality can make significant differences to economic equilibria.

Choosing what to pay attention to

This paper studies static rational inattention problems with multiple actions and multiple shocks. We solve for the optimal signals chosen by agents and provide tools to interpret information processing. By relaxing restrictive assumptions previously used to gain tractability, we allow agents more latitude to choose what to pay attention to. Our applications examine the pricing problem of a monopolist who sells in multiple markets and the portfolio problem of an investor who can invest in multiple assets. The more general models that our methods allow us to solve yield new results. We show conditions under which the multimarket monopolist would optimally choose a uniform pricing strategy, and we show how optimal information processing by rationally inattentive investors can be interpreted as learning about the Sharpe ratio of a diversified portfolio.

Queueing Systems with Rationally Inattentive Customers

Problem definition: Classical models of queueing systems with rational and strategic customers assume queues to be either fully visible or invisible, while service parameters are known with certainty. In practice, however, people only have “partial information” on the service environment, in the sense that they are not able to fully discern prevalent uncertainties. This is because assessing possible delays and rewards is costly, as it requires time, attention, and cognitive capacity, which are all limited. On the other hand, people are also adaptive and endogenously respond to information frictions. Methodology: We develop an equilibrium model for a single-server queueing system with customers having limited attention. Following the theory of rational inattention, we assume that customers optimize their learning strategies by deciding the type and amount of information to acquire and act accordingly while internalizing the associated costs. Results: We establish the existence and uniqueness of a customer equilibrium when customers allocate their attention to learn uncertain queue lengths and delineate the impact of service characteristics. We provide a complete spectrum of the impact of information costs on throughput and show numerically that throughput might be nonmonotone. This is also reflected in social welfare if the firm’s profit margin is high enough, although customer welfare always suffers from information costs. Managerial implications: We identify service settings where service firms and social planners should be most cautious for customers’ limited attention and translate our results to advisable strategies for information provision and service design. For example, we recommend firms to avoid partial hindrance of queue-length information when a low-demand service is not highly valued by customers. For a popular service that customers value reasonably highly, however, partial hindrance of information is particularly advisable. Academic/practical relevance: We propose a microfounded framework for strategic customer behavior in queues that links beliefs, rewards, and information costs. It offers a holistic perspective on the impact of information prevalence (and information frictions) on operational performance and can be extended to analyze richer customer behavior and complex queue structures, rendering it a valuable tool for service design. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2021.1032 .

Asset market equilibrium under rational inattention

We propose a noisy rational expectations equilibrium model of asset markets with rationally inattentive investors. We incorporate any finite number of assets with arbitrary correlation. We also do not restrict the signal form and show that investors optimally choose a single signal, which is a noisy linear combination of all risky assets. This generates comovement of asset prices and contagion of shocks, even when asset payoffs are negatively correlated. The model also provides testable predictions of the impact of risk aversion, aggregate risk, and information capacity on the security market line, the portfolio dispersion, and the abnormal return.

Attentional role of quota implementation

In this paper, we introduce a new role of quotas, e.g. labor market quotas: the attentional role. We study the effect of quota implementation on the attention allocation strategy of a rationally inattentive (RI) manager. We find that quotas induce attention: a RI manager who is forced to fulfill a quota, unlike an unrestricted RI manager, never rejects minority candidates without acquiring information about them. We also demonstrate that in our model quotas are behaviorally equivalent to subsidies. In addition, we analyze different goals that the social planner can achieve by implementing quotas. First, quotas can eliminate statistical discrimination, i.e. make the chances of being hired independent from the group identity. Second, when the hiring manager has inaccurate beliefs about the distribution of candidates' productivities, the social planner can make the manager behave as if she has correct beliefs. Finally, we show how our results can be used to set a quota level that increases the expected value of the chosen candidates.

Rational inattention and the monotone likelihood ratio property

This paper explores the connection between rational inattention and the monotone likelihood ratio property (MLRP). In many economic problems, agents prefer to take a higher action when there is a higher underlying state. It is often assumed that these agents have noisy signals that are strongly correlated with the underlying state, i.e. ordered by the MLRP. Separately, a large literature has recently explored the behavior of rationally inattentive agents. Under some common separability and smoothness assumptions on the class of attention costs, I show that agents will always acquire signals that are ordered by the MLRP within such economic problems if and only if they have attention costs proportional to entropy reduction. With any other attention costs, agents err regarding the relative benefit of actions at different states. Extending to games, I provide conditions under which players first acquire MLRP-ordered signals, and then choose higher actions given higher signals. I then apply these results to independent private-value auctions.

Обзор Гипотезы Рационального Невнимания (Review of the Hypothesis of Rational Inattention)

Russian Abstract: Данная статья знакомит российского читателя с гипотезой рационального невнимания, активно изучаемой в западных исследованиях по экономической тематике. Описан формальный способ ограничения внимания экономического агента с помощью ограничения на поток поступающей к агенту информации. В статье изложены две модели рационально невнимательных агентов: 1) простая однопериодная модель рационально невнимательной фирмы, 2) динамическая модель рационально невнимательной фирмы. Также статья содержит обзор динамической модели общего равновесия (DSGE-модель) с рационально невнимательными фирмами и домохозяйствами, разработанная [Mackowiak, Wiederholt, 2015]. English Abstract: This article introduces the Russian reader to the hypothesis of rational inattention, actively studied in western economic researches. There is the way of describing the limited attention of an economic agent by restricting of information flow coming to the agent. The article also contains the presentation of two models of agents with rational inattention. First model is a simple single-period model of a rationally inattentive firm. Second model is a dynamic model of a rationally inattentive firm. Also, the dynamic stochastic general equilibrium model (DSGE-model) with rationally inattentive firms and households, developed in [Mackowiak, Wiederholt, 2015], is reviewed in this article.

Rational Inattention Dynamics in Stochastic Games: Coordination and Conditioning

Decision-makers that choose information strategies instead of concrete actions elect stochastic choice rules that leave open the potential for errors, which can obfuscate the strategic interactions of players. This article establishes that dynamic, stochastic, games with rationally inattentive agents have Nash equilibria in which players coordinate their choice rules. When these choice rules are compliant with the predisposition of players towards particular actions, the Nash equilibria can be expressed in terms of dynamic logit rules. This result reduces finding Nash equilibria of this type to establishing a joint distribution of actions and states that accommodates the optimal behavior of all players. Logit rule Nash equilibria are used to study an example of strategic coordination, and an example of a zero-sum, strategic conflict game with sequential moves. The resulting equilibria of the second example involve strategies that exhibit conditioning characteristics and can be relevant for applications in principal-agent problems.

Dynamic Rational Inattention and the Phillips Curve

We develop a fast, tractable, and robust method for solving the transition path of dynamic rational inattention problems in linear-quadratic-Gaussian settings. As an application of our general framework, we develop an attention-driven theory of dynamic pricing in which the Phillips curve slope is endogenous to systematic aspects of monetary policy. In our model, when the monetary authority is more committed to stabilizing nominal variables, rationally inattentive firms pay less attention to changes in their input costs, which leads to a flatter Phillips curve and more anchored inflation expectations. This effect, however, is not symmetric. A more dovish monetary policy flattens the Phillips curve in the short-run but generates a steeper Phillips curve in the long-run. In a calibrated version of our general equilibrium model, we find that our mechanism quantifies a 75% decline in the slope of the Phillips curve in the post-Volcker period, relative to the period before it.

Sparking Curiosity or Tipping the Scales? Targeted Advertising to Rationally Inattentive Consumers

This paper argues, in the context of targeted advertising, that receivers' rational inattention and ability to independently acquire information have a non-trivial impact on the sender's optimal disclosure strategy. In our model, a monopolist has an opportunity to launch an advertising campaign and chooses a targeting strategy -- which consumers to send its advertisement to. The consumers are uncertain about and heterogeneous in their valuations of the product, and are rationally inattentive in that they must incur a cost if they want to learn their true valuations. We discover that the firm generally prefers to target consumers who are either indifferent between ignoring and investigating the product, or between investigating and buying it unconditionally. If the firm is uncertain about the consumer appeal of its product, it targets these two distinct groups of consumers simultaneously but may ignore all consumers in between.