Reducing Overconfidence in the Interval Judgments of Experts

Elicitation of expert opinion is important for risk analysis when only limited data are available. Expert opinion is often elicited in the form of subjective confidence intervals; however, these are prone to substantial overconfidence. We investigated the influence of elicitation question format, in particular the number of steps in the elicitation procedure. In a 3‐point elicitation procedure, an expert is asked for a lower limit, upper limit, and best guess, the two limits creating an interval of some assigned confidence level (e.g., 80%). In our 4‐step interval elicitation procedure, experts were also asked for a realistic lower limit, upper limit, and best guess, but no confidence level was assigned; the fourth step was to rate their anticipated confidence in the interval produced. In our three studies, experts made interval predictions of rates of infectious diseases (Study 1, n = 21 and Study 2, n = 24: epidemiologists and public health experts), or marine invertebrate populations (Study 3, n = 34: ecologists and biologists). We combined the results from our studies using meta‐analysis, which found average overconfidence of 11.9%, 95% CI [3.5, 20.3] (a hit rate of 68.1% for 80% intervals)—a substantial decrease in overconfidence compared with previous studies. Studies 2 and 3 suggest that the 4‐step procedure is more likely to reduce overconfidence than the 3‐point procedure (Cohen's d = 0.61, [0.04, 1.18]).     

Sentiments

This paper develops a new theory of fluctuations—one that helps accommodate the notions of “animal spirits” and “market sentiment” in unique‐equilibrium, rational‐expectations, macroeconomic models. To this goal, we limit the communication that is embedded in a neoclassical economy by allowing trading to be random and decentralized. We then show that the business cycle may be driven by a certain type of extrinsic shocks which we call sentiments. These shocks formalize shifts in expectations of economic activity without shifts in the underlying preferences and technologies; they are akin to sunspots, but operate in unique‐equilibrium models. We further show how communication may help propagate these shocks in a way that resembles the spread of fads and rumors and that gives rise to boom‐and‐bust phenomena. We finally illustrate the quantitative potential of our insights within a variant of the RBC model.     

Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information

This paper analyzes a class of games of incomplete information where each agent has private information about her own type, and the types are drawn from an atomless joint probability distribution. The main result establishes existence of pure strategy Nash equilibria (PSNE) under a condition we call the single crossing condition (SCC), roughly described as follows: whenever each opponent uses a nondecreasing strategy (in the sense that higher types choose higher actions), a player's best response strategy is also nondecreasing. When the SCC holds, a PSNE exists in every finite‐action game. Further, for games with continuous payoffs and a continuum of actions, there exists a sequence of PSNE to finite‐action games that converges to a PSNE of the continuum‐action game. These convergence and existence results also extend to some classes of games with discontinuous payoffs, such as first‐price auctions, where bidders may be heterogeneous and reserve prices are permitted. Finally, the paper characterizes the SCC based on properties of utility functions and probability distributions over types. Applications include first‐price, multi‐unit, and all‐pay auctions; pricing games with incomplete information about costs; and noisy signaling games.     

Games with Imperfectly Observable Actions in Continuous Time

This paper investigates a new class of two‐player games in continuous time, in which the players' observations of each other's actions are distorted by Brownian motions. These games are analogous to repeated games with imperfect monitoring in which the players take actions frequently. Using a differential equation, we find the set ℰ(r) of payoff pairs achievable by all public perfect equilibria of the continuous‐time game, where r is the discount rate. The same differential equation allows us to find public perfect equilibria that achieve any value pair on the boundary of the set ℰ(r). These public perfect equilibria are based on a pair of continuation values as a state variable, which moves along the boundary of ℰ(r) during the course of the game. In order to give players incentives to take actions that are not static best responses, the pair of continuation values is stochastically driven by the players' observations of each other's actions along the boundary of the set ℰ(r).     

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.     

Sourcing from Multiple Suppliers for Price‐Dependent Demands

We analyze a model that integrates demand shaping via dynamic pricing and risk mitigation via supply diversification. The firm under consideration replenishes a certain product from a set of capacitated suppliers for a price‐dependent demand in each period. Under deterministic capacities, we derive a multilevel base stock list price policy and establish the optimality of cost‐based supplier selection, that is, ordering from a cheaper source before more expensive ones. With general random capacities, however, neither result holds. While it is optimal to price low for a high inventory level, the optimal order quantities are not monotone with respect to the inventory level. In general, a near reorder‐point policy should be followed. Specifically, there is a reorder point for each supplier such that no order is issued to him when the inventory level is above this point and a positive order is placed almost everywhere when the inventory level is below this point. Under this policy, it may be profitable to order exclusively from the most expensive source. We characterize conditions under which a strict reorder‐point policy and a cost‐based supplier‐selection criterion become optimal. Moreover, we quantify the benefit from dynamic pricing, as opposed to static pricing, and the benefit from multiple sourcing, as opposed to single sourcing. We show that these two strategies exhibit a substitutable relationship. Dynamic pricing is less effective under multiple sourcing than under single sourcing, and supplier diversification is less valuable with price adjustments than without. Under limited supply, dynamic pricing yields a robust, long‐term profit improvement. The value of supply diversification, in contrast, mainly comes from added capacities and is most significant in the short run.     

Optimal Policies for Selling New and Remanufactured Products

Because of environmental and economic reasons, an increasing number of original equipment manufacturers (OEMs) nowadays sell both new and remanufactured products. When both products are available, customers will buy the one that gives them a higher (and non‐negative) utility. Thus, if the firm does not price the products properly, then product cannibalization may arise and its revenue may be adversely impacted. In this paper, we study the pricing problem of a firm that sells both new and remanufactured products over a finite planning horizon. Customer demand processes for both new and remanufactured products are random and price‐sensitive, and product returns (also called cores) are random and remanufactured upon receipt. We characterize the optimal pricing and manufacturing policies that maximize the expected total discounted profit. If new products are made‐to‐order (MTO), we show that when the inventory level of remanufactured product increases, the optimal price of remanufactured product decreases while the price difference between new and remanufactured products increases; however, the optimal selling price of new product may increase or decrease. If new products are made to stock (MTS), then the optimal manufacturing policy is of a base‐stock policy with the base‐stock level decreasing in the remanufactured product inventory level. To understand the potential benefit in implementing an MTO system, we study the difference between the value functions of the MTO and MTS systems, and develop lower and upper bounds for it. Finally, we study several extensions of the base model and show that most of our results extend to those more general settings.     

A Risk Assessment Model for Enterotoxigenic Staphylococcus aureus in Pasteurized Milk: A Potential Route to Source‐Level Inference

This article describes a probabilistic model that quantifies hazards that arise from Staphylococcus aureus in milk that is sold as pasteurized in the United Kingdom. The model is centered on coupled dynamics for S. aureus populations, staphylococcal enterotoxins, and the concentration of alkaline phosphatase throughout the milk chain. The chain includes farm collection and storage of pooled milk, further pooling for off‐farm processing, high temperature short time thermal processing, and possible postprocess contamination. The model is implemented as a Bayesian belief network. The results indicate that milk sold as pasteurized is relatively safe with respect to the hazards associated with S. aureus and that most risk is associated with small scale on‐farm processing. An additional analysis of likelihood ratios shows that alkaline phosphatase concentrations in filler tank milk are a good indicator of potential hazards and that these concentrations, in conjunction with other measurements, can be used effectively to discriminate over possible failure modes. The ability to discriminate over potential failure modes can support preemptive actions, such as maintenance or hygiene, which assist with milk chain management and, over extended periods, accumulate to drive improved safety, efficiency, and security.     

Does Size Matter? A Study of Risk Perceptions of Global Population Growth

The global human population now exceeds 7 billion and is projected to reach 10 billion around 2060. While population growth has been associated with certain benefits (e.g., economies of scale, technological advancements), theoretical models, probabilistic projections, and empirical evidence also indicate that this growth could increase the likelihood of many adverse events (e.g., climate change, resource shortages) and the impact of these events, as more people are exposed to the outcomes. While concerns about these issues are well‐documented in the academic literature, there is little evidence concerning the public's perceptions of the risks associated with global population growth (GPG) and how these perceptions are likely to influence related decisions. To address these issues, we conducted a U.K.‐based study that examined respondents’ risk perceptions of GPG, their willingness to embrace mitigation/precautionary behaviors, and reasons for variations in these two factors. We found that GPG is perceived as a moderate‐to‐high risk, with concerns about the increased likelihood of resource shortages, ecological damage, and violent conflict being foremost. Respondents believed that the worst effects of GPG would arrive around 2050 and would be experienced by the world's poorest people. Respondents who perceived greater levels of risk from GPG were generally those who indicated a greater willingness to embrace mitigation behaviors (e.g., reduce resource consumption) and preventative actions (e.g., support political action to limit growth). We discuss how our findings might be utilized to better manage the potential challenges associated with GPG and we suggest several directions for further research.     

How the Resource-based and the Dynamic Capability Views of the Firm Inform Corporate-level Strategy

This paper explains that the resource‐based view essentially addresses issues of competitive strategy, but by integrating some arguments from its evolutionary version, the dynamic capability view, it can be extended to inform our understanding of corporate‐level strategy. We concentrate on the issue of value creation from corporate centres and ask how the centre can possess or provide resources. The primary dynamic capabilities identified by Teece, Pisano and Shuen (1997) are elaborated into six distinct modes of resource creation. Each mode is considered in relation to a set of organizational design parameters. We then propose resource‐creating configurations that are congruent with respect to the modes and the required states of the design parameters. We point out areas of tension that are likely to arise if corporations try to combine different modes of resource creation. We conclude that corporate centres may possess resources but must display dynamic capabilities otherwise they will destroy shareholder value.     

Pool‐Point Distribution of Zero‐Inventory Products

We study zero‐inventory production‐distribution systems under pool‐point delivery. The zero‐inventory production and distribution paradigm is supported in a variety of industries in which a product cannot be inventoried because of its short shelf life. The advantages of pool‐point (or hub‐and‐spoke) distribution, explored extensively in the literature, include the efficient use of transportation resources and effective day‐to‐day management of operations. The setting of our analysis is as follows: A production facility (plant) with a finite production rate distributes its single product, which cannot be inventoried, to several pool points. Each pool point may require multiple truckloads to satisfy its customers' demand. A third‐party logistics provider then transports the product to individual customers surrounding each pool point. The production rate can be increased up to a certain limit by incurring additional cost. The delivery of the product is done by identical trucks, each having limited capacity and non‐negligible traveling time between the plant and the pool points. Our objective is to coordinate the production and transportation operations so that the total cost of production and distribution is minimized, while respecting the product lifetime and the delivery capacity constraints. This study attempts to develop intuition into zero‐inventory production‐distribution systems under pool‐point delivery by considering several variants of the above setting. These include multiple trucks, a modifiable production rate, and alternative objectives. Using a combination of theoretical analysis and computational experiments, we gain insights into optimizing the total cost of a production‐delivery plan by understanding the trade‐off between production and transportation.     

Some Limitations of “Risk = Threat × Vulnerability × Consequence” for Risk Analysis of Terrorist Attacks

Several important risk analysis methods now used in setting priorities for protecting U.S. infrastructures against terrorist attacks are based on the formula: Risk=Threat×Vulnerability×Consequence. This article identifies potential limitations in such methods that can undermine their ability to guide resource allocations to effectively optimize risk reductions. After considering specific examples for the Risk Analysis and Management for Critical Asset Protection (RAMCAP?) framework used by the Department of Homeland Security, we address more fundamental limitations of the product formula. These include its failure to adjust for correlations among its components, nonadditivity of risks estimated using the formula, inability to use risk‐scoring results to optimally allocate defensive resources, and intrinsic subjectivity and ambiguity of Threat, Vulnerability, and Consequence numbers. Trying to directly assess probabilities for the actions of intelligent antagonists instead of modeling how they adaptively pursue their goals in light of available information and experience can produce ambiguous or mistaken risk estimates. Recent work demonstrates that two‐level (or few‐level) hierarchical optimization models can provide a useful alternative to Risk=Threat×Vulnerability×Consequence scoring rules, and also to probabilistic risk assessment (PRA) techniques that ignore rational planning and adaptation. In such two‐level optimization models, defender predicts attacker's best response to defender's own actions, and then chooses his or her own actions taking into account these best responses. Such models appear valuable as practical approaches to antiterrorism risk analysis.     

Multiperson Bargaining and Strategic Complexity

We investigate the effect of introducing costs of complexity in the n‐person unanimity bargaining game. As is well‐known, in this game every individually rational allocation is sustainable as a Nash equilibrium (also as a subgame perfect equilibrium if players are sufficiently patient and if n & 2). Moreover, delays in agreement are also possible in such equilibria. By limiting ourselves to a plausible notion of complexity that captures length of memory, we find that the introduction of complexity costs (lexicographically with the standard payoffs) does not reduce the range of possible allocations but does limit the amount of delay that can occur in any agreement. In particular, we show that in any n‐player game, for any allocation z, an agreement on z at any period t can be sustained as a Nash equilibrium of the game with complexity costs if and only if t≤n. We use the limit on delay result to establish that, in equilibrium, the strategies implement stationary behavior. Finally, we also show that ‘noisy Nash equilibrium’ with complexity costs sustains only the unique stationary subgame perfect equilibrium allocation.     

The Use of Switching Point and Protection Levels to Improve Revenue Performance in Order‐Driven Production Systems

In a multiproduct order‐driven production system, an organization has to decide how to selectively accept orders and allocate capacity to these orders so as to maximize total profit (TP). In this article, we incorporate the novel concept of switching point in developing three capacity‐allocation with switching point heuristics (CASP_a‐c). Our analysis indicates that all three CASP heuristics outperform the first‐come‐first‐served model and Barut and Sridharan's dynamic capacity‐allocation process (DCAP) model. The best model, CASP_b, has an 8% and 6% average TP improvement over DCAP using the split lot and whole lot policies, respectively. In addition, CASP_b performs particularly well under operating conditions of tight capacity and large price differences between product classes. The introduction of a switching point, which has not been found in previous capacity‐allocation heuristics, provides for a better balance between forward and backward allocation of available capacity and plays a significant role in improving TP.     

Reputation in Continuous‐Time Games

We study reputation dynamics in continuous‐time games in which a large player (e.g., government) faces a population of small players (e.g., households) and the large player's actions are imperfectly observable. The major part of our analysis examines the case in which public signals about the large player's actions are distorted by a Brownian motion and the large player is either a normal type, who plays strategically, or a behavioral type, who is committed to playing a stationary strategy. We obtain a clean characterization of sequential equilibria using ordinary differential equations and identify general conditions for the sequential equilibrium to be unique and Markovian in the small players' posterior belief. We find that a rich equilibrium dynamics arises when the small players assign positive prior probability to the behavioral type. By contrast, when it is common knowledge that the large player is the normal type, every public equilibrium of the continuous‐time game is payoff‐equivalent to one in which a static Nash equilibrium is played after every history. Finally, we examine variations of the model with Poisson signals and multiple behavioral types.     

The Strategic Role of Third‐Party Marketplaces in Retailing

Retailers are increasingly adopting a dual‐format model. In addition to acting as traditional merchants (buying and reselling goods), these retailers provide a platform for third‐party (3P) sellers to access and compete for the same customers. We investigate the strategic rationale for a retailer to introduce a 3P marketplace. Our analysis provides insights into the growing prevalence of 3P marketplaces. We show that by committing to having an active 3P marketplace, the retailer creates an “outside option” that improves its bargaining position in negotiations with the manufacturer. This can explain the increasing prevalence of such marketplaces. On the other hand, the manufacturer would prefer to eliminate the retailer's outside option and should seek to limit or prevent sales through 3P marketplaces. This is consistent with actions that several manufacturers have taken to limit such sales. Interestingly, if the manufacturer fails to eliminate sales of competing products through the 3P marketplace, then the best strategy for the manufacturer is to allow the retailer to dictate the terms of their contract. This is because a powerful retailer will rely less on its outside option in generating profit, and therefore it will increase the fees charged to 3P sellers and soften the competition between 3P sellers and the manufacturer. The decrease in competition will lead to an increase in the value of outside option of the manufacturer and improve its profit. Additionally, we find that the presence of a 3P marketplace benefits consumers, but this benefit diminishes as the retailer becomes more powerful.     

Using In Vitro High‐Throughput Screening Data for Predicting Benzo[k]Fluoranthene Human Health Hazards

Today there are more than 80,000 chemicals in commerce and the environment. The potential human health risks are unknown for the vast majority of these chemicals as they lack human health risk assessments, toxicity reference values, and risk screening values. We aim to use computational toxicology and quantitative high‐throughput screening (qHTS) technologies to fill these data gaps, and begin to prioritize these chemicals for additional assessment. In this pilot, we demonstrate how we were able to identify that benzo[k]fluoranthene may induce DNA damage and steatosis using qHTS data and two separate adverse outcome pathways (AOPs). We also demonstrate how bootstrap natural spline‐based meta‐regression can be used to integrate data across multiple assay replicates to generate a concentration–response curve. We used this analysis to calculate an in vitro point of departure of 0.751 μM and risk‐specific in vitro concentrations of 0.29 μM and 0.28 μM for 1:1,000 and 1:10,000 risk, respectively, for DNA damage. Based on the available evidence, and considering that only a single HSD17B4 assay is available, we have low overall confidence in the steatosis hazard identification. This case study suggests that coupling qHTS assays with AOPs and ontologies will facilitate hazard identification. Combining this with quantitative evidence integration methods, such as bootstrap meta‐regression, may allow risk assessors to identify points of departure and risk‐specific internal/in vitro concentrations. These results are sufficient to prioritize the chemicals; however, in the longer term we will need to estimate external doses for risk screening purposes, such as through margin of exposure methods.     

Communication With Unknown Perspectives

Consider a group of individuals with unobservable perspectives (subjective prior beliefs) about a sequence of states. In each period, each individual receives private information about the current state and forms an opinion (a posterior belief). She also chooses a target individual and observes the target's opinion. This choice involves a trade‐off between well‐informed targets, whose signals are precise, and well‐understood targets, whose perspectives are well known. Opinions are informative about the target's perspective, so observed individuals become better understood over time. We identify a simple condition under which long‐run behavior is history independent. When this fails, each individual restricts attention to a small set of experts and observes the most informed among these. A broad range of observational patterns can arise with positive probability, including opinion leadership and information segregation. In an application to areas of expertise, we show how these mechanisms generate own field bias and large field dominance.     

Context‐Specific,Scenario‐Based Risk Scales

Reacting to an emergency requires quick decisions under stressful and dynamic conditions. To react effectively, responders need to know the right actions to take given the risks posed by the emergency. While existing research on risk scales focuses primarily on decision making in static environments with known risks, these scales may be inappropriate for conditions where the decision maker's time and mental resources are limited and may be infeasible if the actual risk probabilities are unknown. In this article, we propose a method to develop context‐specific, scenario‐based risk scales designed for emergency response training. Emergency scenarios are used as scale points, reducing our dependence on known probabilities; these are drawn from the targeted emergency context, reducing the mental resources required to interpret the scale. The scale is developed by asking trainers/trainees to rank order a range of risk scenarios and then aggregating these orderings using a Kemeny ranking. We propose measures to assess this aggregated scale's internal consistency, reliability, and validity, and we discuss how to use the scale effectively. We demonstrate our process by developing a risk scale for subsurface coal mine emergencies and test the reliability of the scale by repeating the process, with some methodological variations, several months later.     

Poverty and Self‐Control

We argue that poverty can perpetuate itself by undermining the capacity for self‐control. In line with a distinguished psychological literature, we consider modes of self‐control that involve the self‐imposed use of contingent punishments and rewards. We study settings in which consumers with quasi‐hyperbolic preferences confront an otherwise standard intertemporal allocation problem with credit constraints. Our main result demonstrates that low initial assets can limit self‐control, trapping people in poverty, while individuals with high initial assets can accumulate indefinitely. Thus, even temporary policies that initiate accumulation among the poor may be effective. We examine implications concerning the effect of access to credit on saving, the demand for commitment devices, the design of financial accounts to promote accumulation, and the variation of the marginal propensity to consume across income from different sources. We also explore the nature of optimal self‐control, demonstrating that it has a simple and behaviorally plausible structure that is immune to self‐renegotiation.