SAMPLING AS A SOLUTION METHODOLOGY

This paper examines the use of sampling procedures as a solution methodology for large combinatorial problems. Three sampling strategies are investigated: random sampling (each alternative is equally likely), biased sampling (alternatives' probabilities are biased by specified criteria), and improvement sampling (alternatives' probabilities are dynamically changed based upon new information). These three methodologies are illustrated and compared on the basis of solution quality and computer time requirements.     

Measuring Expectations

To predict choice behavior, the standard practice of economists has been to infer decision processes from data on observed choices. When decision makers act with partial information, economists typically assume that persons form probabilistic expectations for unknown quantities and maximize expected utility. Observed choices may be consistent with many alternative specifications of preferences and expectations, so researchers commonly assume particular sorts of expectations. It would be better to measure expectations in the form called for by modern economic theory; that is, subjective probabilities. Data on expectations can be used to relax or validate assumptions about expectations. Since the early 1990's, economists have increasingly undertaken to elicit from survey respondents probabilistic expectations of significant personal events. This article discusses the history underlying the new literature, describes some of what has been learned thus far, and looks ahead towards making further progress.     

Resource Distribution in Multiple Attacks with Imperfect Detection of the Attack Outcome

This article extends the previous research of consecutive attacks strategy by assuming that an attacker observes the outcome of each attack imperfectly. With given probabilities it may wrongly identify a destroyed target as undestroyed, and wrongly identify an undestroyed target as destroyed. The outcome of each attack is determined by a contest success function that depends on the amount of resources allocated by the defender and the attacker to each attack. The article suggests a probabilistic model of the multiple attacks and analyzes how the target destruction probability and the attacker's relative resource expenditure are impacted by the two probabilities of incorrect observation, the attacker's and defender's resource ratio, the contest intensity, the number of attacks, and the resource distribution across attacks. We analyze how the attacker chooses the number of attacks, the attack stopping rule, and the optimal resource distribution across attacks to maximize its utility.     

Understanding managers' preferences for internal markets versus business planning: A comparative study of German and U.S. managers

Internal markets and centralized business planning are alternative organizational designs for coordinating the economic activities within a firm. While some preliminary theory about when to use each exists in the literature, little is known about how managers understand and decide when to use one or the other. The study develops and tests in samples of German and U.S. managers a preliminary theory about factors that influence the preferences of managers for internal markets or planning as alternative modes of coordination. Managers' preferences are influenced by key constructs of internal markets and planning theory (the perceived limits of planning, speed and efficiency of markets, motivation potential of markets), but also by differences in their institutional contexts (national government and business context, company culture, and recent company experience with planning and internal markets). The study is the first to explore the substitutability of internal markets and planning within the strategic decision process of managers, closer to where it becomes reality.     

Evaluating new product decision processes

The development of a new product is often a sequential-decision process with many available stages at which the product may take any one of a number of alternate courses of action. This paper identifies an efficient algorithm for solving this sequential-decision process. A computer program, involving the algorithm, has been written to solve problems containing up to one thousand stages. Input into the program includes the subjective probabilities of success for each decision branch, the cost associated with each decision stage and level, the rate for discounting all monetary values to the present plus an indicator for each decision stage and level of the desired decision criterion. The algorithm utilizes the dynamic-programming solution approach. The output of the algorithm contains the minimum, or maximum, expected discounted decision values for each stage and level of the network. The algorithm and computer program have been primarily utilized in the pharmaceutical industry. An illustrative, exemplary use of the algorithm in this industry is presented.     

On Forward Induction

A player's pure strategy is called relevant for an outcome of a game in extensive form with perfect recall if there exists a weakly sequential equilibrium with that outcome for which the strategy is an optimal reply at every information set it does not exclude. The outcome satisfies forward induction if it results from a weakly sequential equilibrium in which players' beliefs assign positive probability only to relevant strategies at each information set reached by a profile of relevant strategies. We prove that if there are two players and payoffs are generic, then an outcome satisfies forward induction if every game with the same reduced normal form after eliminating redundant pure strategies has a sequential equilibrium with an equivalent outcome. Thus in this case forward induction is implied by decision‐theoretic criteria.     

AN EMPIRICAL EXAMINATION OF SOCIAL POWER IN TERMS OF DECISION THEORY1

The paper presents an extension of decision theory to the analysis of social power. The power of a person, A, over another person, B, is viewed in terms of the effect A has on B's decision. The analysis is based on the idea that B's decision regarding the performance of alternative behaviors is a function of 1) B's utility for the consequences of the behaviors and 2) B's subjective probabilities that the behaviors will lead to these consequences. In these terms, A's power over B lies in A's ability to mediate various consequences for B, contingent upon B's compliance or noncompliance. Subjects were asked to consider eight situations in which hypothetical individuals had to make a choice between two courses of action. In each situation another person (A) was attempting to induce the hypothetical individual (B) to choose one of the alternatives, while various situational factors were influencing B to choose the other alternative. The subjects were asked to consider B's utilities and subjective probabilities in each situation and to indicate whether or not B should comply with A and to make ratings of A's power. The decision theory analysis did well in predicting whether or not subjects would indicate that B should comply with A. Also, subjects generally were able to correctly specify whether A or the situational factors had more influence over B's decision. Finally, the subjects' ratings of A's power in the eight situations were highly related to the decision theoretic measure of power.     

Ambiguity Aversion,Robustness, and the Variational Representation of Preferences

We characterize, in the Anscombe–Aumann framework, the preferences for which there are a utility functionu on outcomes and an ambiguity indexc on the set of probabilities on the states of the world such that, for all acts f and g, . The function u represents the decision maker's risk attitudes, while the index c captures his ambiguity attitudes. These preferences include the multiple priors preferences of Gilboa and Schmeidler and the multiplier preferences of Hansen and Sargent. This provides a rigorous decision‐theoretic foundation for the latter model, which has been widely used in macroeconomics and finance.     

MODEL UNCERTAINTY

We study decision problems in which consequences of the various alternative actions depend on states determined by a generative mechanism representing some natural or social phenomenon. Model uncertainty arises because decision makers may not know this mechanism. Two types of uncertainty result, a state uncertainty within models and a model uncertainty across them. We discuss some two‐stage static decision criteria proposed in the literature that address state uncertainty in the first stage and model uncertainty in the second (by considering subjective probabilities over models). We consider two approaches to the Ellsberg‐type phenomena characteristic of such decision problems: a Bayesian approach based on the distinction between subjective attitudes toward the two kinds of uncertainty; and a non‐Bayesian approach that permits multiple subjective probabilities. Several applications are used to illustrate concepts as they are introduced.     

THE SEU CALCULUS: EFFECTS OF RESPONSE MODE,SEX, AND SEX ROLE ON UNCERTAIN DECISIONS *

Subjects were instructed on how to use simple subjective probability and utility scales, and they were asked to actively role-play a decision maker in seven risk-dilemma situations. Each scenario provided subjects with specific subjective expected utility (SEU) information for both a certain and uncertain decision alternative, but left out one critical SEU component. Subjects supplied either the lowest probability or the lowest utility for success that they found necessary before they would select the uncertain over the certain alternative in each dilemma. Three experiments examined: (a) the degree to which Ss' estimations deviated from a pattern predicted by SEU models; (b) differences in choice patterns induced by response format variations (e.g., probability vs. utility estimation); (c) the effects of sex of S; and (d) the effects of the sex-role framing of the decision problems. Ss generally chose in accord with SEU maximization principles and did so with decreasing deviations from theoretical values as practice over situations increased (Experiments I, II and III). Decisions were initially more conservative on items requesting probability estimates (Experiment I), but this effect washed out over situations. Sex differences were revealed (Experiments I and III), but in limited fashion. Rather, a replicable (Experiments I, II and III) sex-by-sex role appropriateness by response format interaction was found, in which females responded “rationally” under both probability and utility estimation conditions and under both role sets (male and female). Males, however, responded extremely conservatively under female-framed, probability estimate conditions. Ss' choices were stable over a three-week interval (Experiment III).     

A Study on a Sequential One‐Defender‐N‐Attacker Game

Government usually faces threat from multiple attackers. However, in the literature, researchers often model attackers as one monolithic player who chooses whether to attack, how much investment to spend, and on which target, instead of treating multiple attackers as independent agents. This modeling strategy may potentially cause suboptimal defense investment if the attackers have vastly different interests and preferences and may not be combined as one in theory. In this article, we develop a sequential game with complete information. This model considers one defender explicitly dealing with multiple unmergeable attackers. Thorough numerical experiments are conducted using ratio and exponential contest success functions under different scenarios. The result is also contrasted with the corresponding single attacker model to study the effect of mishandling multiple attackers. The propositions and observations drawn from the numerical experiments provide insights for government decision making with a better understanding of the attackers' behavior.     

多属性群决策的混合结构偏好识别与融合方法

为有效应对现有群决策偏好一致性检验方法的系列弊端,针对目前群决策情景所展现的决策导向多元、方案属性构成迥异和偏好结构复杂等特征,在解析群决策偏好一致性判定复杂性、刻画群决策偏好信息表征假设情景的基础上,对常规多属性群决策问题进行公理化描述。依据从方案层面到属性层面的整体决策信息判定策略,给出决策导向层面的整体判断偏好一致性检验方法、决策群体偏好类型识别方法、同种偏好内部及偏好间累积判断偏差求解方法、偏好整体相对一致性检验方法和多轮次非一致性决策信息调整策略。案例应用结果表明,上述所构建的方法和策略有效、可行,能够为决策导向多元、备选方案差异显著情景下的混合结构偏好一致性检验、调整与集结提供借鉴。     

Overcoming Learning Aversion in Evaluating and Managing Uncertain Risks

Decision biases can distort cost‐benefit evaluations of uncertain risks, leading to risk management policy decisions with predictably high retrospective regret. We argue that well‐documented decision biases encourage learning aversion, or predictably suboptimal learning and premature decision making in the face of high uncertainty about the costs, risks, and benefits of proposed changes. Biases such as narrow framing, overconfidence, confirmation bias, optimism bias, ambiguity aversion, and hyperbolic discounting of the immediate costs and delayed benefits of learning, contribute to deficient individual and group learning, avoidance of information seeking, underestimation of the value of further information, and hence needlessly inaccurate risk‐cost‐benefit estimates and suboptimal risk management decisions. In practice, such biases can create predictable regret in selection of potential risk‐reducing regulations. Low‐regret learning strategies based on computational reinforcement learning models can potentially overcome some of these suboptimal decision processes by replacing aversion to uncertain probabilities with actions calculated to balance exploration (deliberate experimentation and uncertainty reduction) and exploitation (taking actions to maximize the sum of expected immediate reward, expected discounted future reward, and value of information). We discuss the proposed framework for understanding and overcoming learning aversion and for implementing low‐regret learning strategies using regulation of air pollutants with uncertain health effects as an example.     

SUBJECTIVE EVALUATIONS FOR PRODUCT DESIGN DECISIONS

This paper presents a simple methodology to enable a firm to incorporate consumers' subjective evaluations early into the concept screening stage of a new product introduction process. The methodology involves eliciting ranked preference judgments toward a set of alternative product concepts, each described as a profile of attributes and derived from an interval-scaled utility score using Thurstone's comparative judgment model. The derived utility scores are then decomposed into simple effects attributable to each of the attributes, thus yielding functional representations of consumer preferences. Mathematical models are developed to utilize the functions to determine the best concept. Empirical illustrations are provided for application of the methodology.     

Managerial Use of Debt to Fund Municipal Government Risks*

In recent years, managers of municipalities have been forced to reevaluate the cost-effectiveness of their risk management strategy. In many cases, individual or groups of municipalities (pools) finance a self-insurance plan through the issuance of debt. However, no decision-making methodology for cost-effectively structuring the debt issue presently exists. Utilizing a math programming model, we examine a self-insurance alternative to conventional insurance that uses tax-exempt debt supplemented by taxable borrowing to finance a municipality's or pool's liability exposure. We implement our optimization model with actuarial and financial data from an intergovernmental risk pool (IRP) in the state of California, and simulate the effect of the trade-offs important to sound managerial decision making. We find that significant savings are realized by using a self-insurance plan rather than purchasing conventional insurance. We also find that managerial goals and risk preferences impact the decision when revenue flows are insufficient by themselves to reasonably fund expected losses.     

Robustness and Separation in Multidimensional Screening

A principal wishes to screen an agent along several dimensions of private information simultaneously. The agent has quasilinear preferences that are additively separable across the various components. We consider a robust version of the principal's problem, in which she knows the marginal distribution of each component of the agent's type, but does not know the joint distribution. Any mechanism is evaluated by its worst‐case expected profit, over all joint distributions consistent with the known marginals. We show that the optimum for the principal is simply to screen along each component separately. This result does not require any assumptions (such as single crossing) on the structure of preferences within each component. The proof technique involves a generalization of the concept of virtual values to arbitrary screening problems. Sample applications include monopoly pricing and a stylized dynamic taxation model.     

A DECISION THEORY EXAMPLE IN FOOTBALL

In the 1967 Harvard-Cornell football game, Harvard was ahead 14–0 late in the game when Cornell scored two touchdowns. On both occasions, Cornell tried and failed on the two-point conversion attempt and lost the game 14–12. Postgame arguments were divided on the merits of Cornell's strategy. For this frequently occurring scenario in college football, we derive a maximum expected utility decision rule for the decision of kicking versus running/passing based on the relative utility of a win, a tie, or a loss and the probabilities of success with a kick as opposed to a run/pass.     

Parenting With Style: Altruism and Paternalism in Intergenerational Preference Transmission

We develop a theory of parent‐child relations that rationalizes the choice between alternative parenting styles (as set out in Baumrind, 1967). Parents maximize an objective function that combines Beckerian altruism and paternalism towards children. They can affect their children's choices via two channels: either by influencing children's preferences or by imposing direct restrictions on their choice sets. Different parenting styles (authoritarian, authoritative, and permissive) emerge as equilibrium outcomes and are affected both by parental preferences and by the socioeconomic environment. Parenting style, in turn, feeds back into the children's welfare and economic success. The theory is consistent with the decline of authoritarian parenting observed in industrialized countries and with the greater prevalence of more permissive parenting in countries characterized by low inequality.     

Comparing methods for weighting decision criteria

Several metbods have been proposed to weight decision criteria. In this field study a decision group, like that used by public agencies, was formed to establish project priorities. The decision group used a variety of criteria weighting methods to study how these methods influence the magnitude of the weights assigned by members of the decision group. Direct criteria weighting methods (scaling, rank-weight, point assignment and odds procedures) and an indirect approach (weights derived from hypothetical projects) were considered. The study compared the methods in terms of the magnitude of the weights assigned, the variance in weights among members of the decision group, and the similarity of the decisions based on weights assigned by each method. The time to apply each method and the preferences of the decision makers were also determined. The linear rating scale that defined the meaning of scale increments, called an ‘anchored ratin scale’, was found to be favorably received and efficient and led to the most defensible decisions.     

Process Tracing Analysis of Hurricane Information Displays

To study people's processing of hurricane forecast advisories, we conducted a computer‐based experiment that examined 11 research questions about the information seeking patterns of students assuming the role of a county emergency manager in a sequence of six hurricane forecast advisories for each of four different hurricanes. The results show that participants considered a variety of different sources of information—textual, graphic, and numeric—when tracking hurricanes. Click counts and click durations generally gave the same results but there were some significant differences. Moreover, participants’ information search strategies became more efficient over forecast advisories and with increased experience tracking the four hurricanes. These changes in the search patterns from the first to the fourth hurricane suggest that the presentation of abstract principles in a training manual was not sufficient for them to learn how to track hurricanes efficiently but they were able to significantly improve their search efficiency with a modest amount (roughly an hour) of practice. Overall, these data indicate that information search patterns are complex and deserve greater attention in studies of dynamic decision tasks.