Temptation and Self‐Control

We study a two‐period model where ex ante inferior choice may tempt the decision‐maker in the second period. Individuals have preferences over sets of alternatives that represent second period choices. Our axioms yield a representation that identifies the individual's commitment ranking, temptation ranking, and cost of self‐control. An agent has a preference for commitment if she strictly prefers a subset of alternatives to the set itself. An agent has self‐control if she resists temptation and chooses an option with higher ex ante utility. We introduce comparative measures of preference for commitment and self‐control and relate them to our representations.     

Temptation and Revealed Preference

Gul and Pesendorfer (2001) model the static behavior of an agent who ranks menus prior to the experience of temptation. This paper models the dynamic behavior of an agent whose ranking of menus itself is subject to temptation. The representation for the agent's dynamically inconsistent choice behavior views him as possessing a dynamically consistent view of what choices he “should” make (a normative preference) and being tempted by menus that contain tempting alternatives. Foundations for the model require a departure from Gul and Pesendorfer's idea that temptation creates a preference for commitment. Instead, it is hypothesized that distancing an agent from the consequences of his choices separates normative preference and temptation.     

Self‐Control and the Theory of Consumption

To study the behavior of agents who are susceptible to temptation in infinite horizon consumption problems under uncertainty, we define and characterize dynamic self‐control (DSC) preferences. DSC preferences are recursive and separable. In economies with DSC agents, equilibria exist but may be inefficient; in such equilibria, steady state consumption is independent of initial endowments and increases in self‐control. Increasing the preference for commitment while keeping self‐control constant increases the equity premium. Removing nonbinding constraints changes equilibrium allocations and prices. Debt contracts can be sustained even if the only feasible punishment for default is the termination of the contract.     

Preference for Flexibility and Random Choice

We study a two‐stage model where the agent has preferences over menus as in Dekel, Lipman, and Rustichini (2001) in the first period and then makes random choices from menus as in Gul and Pesendorfer (2006) in the second period. Both preference for flexibility in the first period and strictly random choices in the second period can be, respectively, rationalized by subjective state spaces. Our main result characterizes the representation where the two state spaces align, so the agent correctly anticipates her future choices. The joint representation uniquely identifies probabilities over subjective states and magnitudes of utilities across states. We also characterize when the agent completely overlooks some subjective states that realize at the point of choice.     

Anticipating Regret: Why Fewer Options May Be Better

We study preferences over menus which can be represented as if the agent selects an alternative from a menu and experiences regret if her choice is ex post inferior. Since regret arises from comparisons between the alternative selected and the other available alternatives, our axioms reflect the agent's desire to limit her options. We prove that our representation is essentially unique. We also introduce two measures of comparative regret attitudes and relate them to our representation. Finally, we explore the formal connection between the present work and the literature on temptation.     

MEASURING SELF‐CONTROL PROBLEMS: A STRUCTURAL ESTIMATION

Abstract We adopt a two‐stage Method of Simulated Moments to estimate the preference parameters in a life‐cycle consumption‐saving model augmented with temptation disutility. Our approach estimates the parameters from the comparison between simulated moments with empirical moments observed in the US Survey of Consumer Finances; to identify the parameters we consider moments from liquid and illiquid asset holdings at different ages. We find evidence of a small but significantly positive degree of temptation. The temptation model predicts consumption choices similar to the model with standard preferences, and holdings of liquid and illiquid assets closer to those observed in the empirical data.     

Random Expected Utility

We develop and analyze a model of random choice and random expected utility. A decision problem is a finite set of lotteries that describe the feasible choices. A random choice rule associates with each decision problem a probability measure over choices. A random utility function is a probability measure over von Neumann–Morgenstern utility functions. We show that a random choice rule maximizes some random utility function if and only if it is mixture continuous, monotone (the probability that a lottery is chosen does not increase when other lotteries are added to the decision problem), extreme (lotteries that are not extreme points of the decision problem are chosen with probability 0), and linear (satisfies the independence axiom).     

Vertical Integration with Price‐Setting Competitive Newsvendors*

This article addresses the problem of distribution channel design under demand uncertainty. We consider two manufacturers, each producing a substitutable product and selling it through either a decentralized or an integrated retail store, which is modeled as a price‐setting newsvendor. A multiplicative demand function incorporating a random shock term is assumed. Of primary interest is how demand uncertainty and production cost affect the equilibrium distribution channel structure. Results indicate the following: On the one hand, if the random shock term is uniformly distributed on [0, x], then the equilibrium design does not depend on the variance of the shock. On the other hand, if the random shock term is uniformly distributed on [1 −r, 1 +r], then the equilibrium design does depend on the variance of the shock. In particular, an increase in r favors the integrated structure where both channels are integrated and hurts the decentralized configuration where both channels are decentralized. Additionally, we explain the qualitative similarities and differences between the structural properties of the equilibrium distribution channel structure when demand is, and is not, uncertain. We also establish that production cost always favors the decentralized structure, while it hurts the integrated one. One important managerial implication of our study is that, by reducing the number of decisions made in supply chains, the impact of demand uncertainty can be controlled to a certain extent.     

Equivalence Between Out‐of‐Sample Forecast Comparisons and Wald Statistics

We demonstrate the asymptotic equivalence between commonly used test statistics for out‐of‐sample forecasting performance and conventional Wald statistics. This equivalence greatly simplifies the computational burden of calculating recursive out‐of‐sample test statistics and their critical values. For the case with nested models, we show that the limit distribution, which has previously been expressed through stochastic integrals, has a simple representation in terms of χ²‐distributed random variables and we derive its density. We also generalize the limit theory to cover local alternatives and characterize the power properties of the test.     

Probability and Possibility‐Based Representations of Uncertainty in Fault Tree Analysis

Expert knowledge is an important source of input to risk analysis. In practice, experts might be reluctant to characterize their knowledge and the related (epistemic) uncertainty using precise probabilities. The theory of possibility allows for imprecision in probability assignments. The associated possibilistic representation of epistemic uncertainty can be combined with, and transformed into, a probabilistic representation; in this article, we show this with reference to a simple fault tree analysis. We apply an integrated (hybrid) probabilistic‐possibilistic computational framework for the joint propagation of the epistemic uncertainty on the values of the (limiting relative frequency) probabilities of the basic events of the fault tree, and we use possibility‐probability (probability‐possibility) transformations for propagating the epistemic uncertainty within purely probabilistic and possibilistic settings. The results of the different approaches (hybrid, probabilistic, and possibilistic) are compared with respect to the representation of uncertainty about the top event (limiting relative frequency) probability. Both the rationale underpinning the approaches and the computational efforts they require are critically examined. We conclude that the approaches relevant in a given setting depend on the purpose of the risk analysis, and that further research is required to make the possibilistic approaches operational in a risk analysis context.     

Entry Deterrence of Capacitated Competition Using Price and Non‐Price Strategies

We analyze the role of pricing and branding in an incumbent firm's decision when facing competition from an entrant firm with limited capacity. We do so by studying two price competition models (Stackelberg and Nash), where we consider the incumbent's entry‐deterrence pricing strategy based on a potential entrant's capacity size. In an extension, we also study a branding model, where the incumbent firm, in addition to pricing, can also invest in influencing market preference for its product. With these models, we study conditions under which the incumbent firm may block the entrant (i.e., prevent entry without any market actions), deter the entrant (i.e., stop entry with suitable market actions) or accommodate the entrant (i.e., allow entry and compete), and how the entrant will allocate its limited capacity across its own and the new market, if entry occurs. We also study the timing difference between the two different dynamics of the price competition models and find that the incumbent's first‐mover advantage benefits both the incumbent and the entrant. Interestingly, the entrant firm's profits are not monotonically increasing in its capacity even when it is costless to build capacity. In the branding model, we show that in some cases, the incumbent may even increase its price and successfully deter entry by investing in consumer's preference for its product. Finally, we incorporate demand uncertainty into our model and show that the incumbent benefits from demand uncertainty while the entrant may be worse off depending on the magnitude of demand uncertainty and its capacity.     

Objective and Subjective Rationality in a Multiple Prior Model

A decision maker (DM) is characterized by two binary relations. The first reflects choices that are rational in an “objective” sense: the DM can convince others that she is right in making them. The second relation models choices that are rational in a “subjective” sense: the DM cannot be convinced that she is wrong in making them. In the context of decision under uncertainty, we propose axioms that the two notions of rationality might satisfy. These axioms allow a joint representation by a single set of prior probabilities and a single utility index. It is “objectively rational” to choose f in the presence of g if and only if the expected utility of f is at least as high as that of g given each and every prior in the set. It is “subjectively rational” to choose f rather than g if and only if the minimal expected utility of f (with respect to all priors in the set) is at least as high as that of g. In other words, the objective and subjective rationality relations admit, respectively, a representation à la Bewley (2002) and à la Gilboa and Schmeidler (1989). Our results thus provide a bridge between these two classic models, as well as a novel foundation for the latter.     

An Empirical Model of Perceived Mortality Risks for Selected U.S. Arsenic Hot Spots

Researchers have long recognized that subjective perceptions of risk are better predictors of choices over risky outcomes than science‐based or experts’ assessments of risk. More recent work suggests that uncertainty about risks also plays a role in predicting choices and behavior. In this article, we develop and estimate a formal model for an individual's perceived health risks associated with arsenic contamination of his or her drinking water. The modeling approach treats risk as a random variable, with an estimable probability distribution whose variance reflects uncertainty. The model we estimate uses data collected from a survey given to a sample of people living in arsenic‐prone areas in the United States. The findings from this article support the fact that scientific information is essential to explaining the mortality rate perceived by the individuals, but uncertainty about the probability remains significant.     

Random Choice and Private Information

We consider an agent who chooses an option after receiving some private information. This information, however, is unobserved by an analyst, so from the latter's perspective, choice is probabilistic or random. We provide a theory in which information can be fully identified from random choice. In addition, the analyst can perform the following inferences even when information is unobservable: (1) directly compute ex ante valuations of menus from random choice and vice versa, (2) assess which agent has better information by using choice dispersion as a measure of informativeness, (3) determine if the agent's beliefs about information are dynamically consistent, and (4) test to see if these beliefs are well‐calibrated or rational.     

Menu‐Dependent Stochastic Feasibility

We examine the role of stochastic feasibility in consumer choice using a random conditional choice set rule (RCCSR) and uniquely characterize the model from conditions on stochastic choice data. Feasibility is modeled to permit correlation in availability of alternatives. This provides a natural way to examine substitutability/complementarity. We show that an RCCSR generalizes the random consideration set rule of [Manzini and Mariotti, 2014]. We then relate this model to existing literature. In particular, an RCCSR is not a random utility model.     

A Unique Costly Contemplation Representation

We study preferences over menus which can be represented as if the individual is uncertain of her tastes, but is able to engage in costly contemplation before selecting an alternative from a menu. Since contemplation is costly, our key axiom, aversion to contingent planning, reflects the individual's preference to learn the menu from which she will be choosing prior to engaging in contemplation about her tastes for the alternatives. Our representation models contemplation strategies as subjective signals over a subjective state space. The subjectivity of the state space and the information structure in our representation makes it difficult to identify them from the preference. To overcome this issue, we show that each signal can be modeled in reduced form as a measure over ex post utility functions without reference to a state space. We show that in this reduced‐form representation, the set of measures and their costs are uniquely identified. Finally, we provide a measure of comparative contemplation costs and characterize the special case of our representation where contemplation is costless.     

Timing and Self‐Control

The standard dual‐self model of self‐control, with a shorter‐run self who cares only about the current period, is excessively sensitive to the timing of decisions and to the interpolation of additional “no‐action” time periods in between the dates when decisions are made. We show that when the shorter‐run self is not completely myopic, this excess sensitivity goes away. To accommodate the combination of short time periods and convex costs of self‐control, we introduce a cognitive resource variable that tracks how the control cost depends on the self‐control that has been used in the recent past. We consider models with both linear and convex control costs, illustrating the theory through a series of examples. We examine when opportunities to consume will be avoided or delayed, and we consider the way in which the marginal interest declines with delay.     

Nonparametric Test for Causality with Long‐range Dependence

This paper introduces a nonparametric Granger‐causality test for covariance stationary linear processes under, possibly, the presence of long‐range dependence. We show that the test is consistent and has power against contiguous alternatives converging to the parametric rate T^−1/2. Since the test is based on estimates of the parameters of the representation of a VAR model as a, possibly, two‐sided infinite distributed lag model, we first show that a modification of Hannan's (1963, 1967) estimator is root‐ T consistent and asymptotically normal for the coefficients of such a representation. When the data are long‐range dependent, this method of estimation becomes more attractive than least squares, since the latter can be neither root‐ T consistent nor asymptotically normal as is the case with short‐range dependent data.     

Perceived Ambiguity and Relevant Measures

We axiomatize preferences that can be represented by a monotonic aggregation of subjective expected utilities generated by a utility function and some set of i.i.d. probability measures over a product state space, S^∞. For such preferences, we define relevant measures, show that they are treated as if they were the only marginals possibly governing the state space, and connect them with the measures appearing in the aforementioned representation. These results allow us to interpret relevant measures as reflecting part of perceived ambiguity, meaning subjective uncertainty about probabilities over states. Under mild conditions, we show that increases or decreases in ambiguity aversion cannot affect the relevant measures. This property, necessary for the conclusion that these measures reflect only perceived ambiguity, distinguishes the set of relevant measures from the leading alternative in the literature. We apply our findings to a number of well‐known models of ambiguity‐sensitive preferences. For each model, we identify the set of relevant measures and the implications of comparative ambiguity aversion.     

Branch‐and‐Price Methods for Prescribing Profitable Upgrades of High‐Technology Products with Stochastic Demands*

This paper develops a model that can be used as a decision support aid, helping manufacturers make profitable decisions in upgrading the features of a family of high‐technology products over its life cycle. The model integrates various organizations in the enterprise: product design, marketing, manufacturing, production planning, and supply chain management. Customer demand is assumed random and this uncertainty is addressed using scenario analysis. A branch‐and‐price (B&P) solution approach is devised to optimize the stochastic problem effectively. Sets of random instances are generated to evaluate the effectiveness of our solution approach in comparison with that of commercial software on the basis of run time. Computational results indicate that our approach outperforms commercial software on all of our test problems and is capable of solving practical problems in reasonable run time. We present several examples to demonstrate how managers can use our models to answer “what if” questions.