Stochastic Choice and Revealed Perturbed Utility

Perturbed utility functions—the sum of expected utility and a nonlinear perturbation function—provide a simple and tractable way to model various sorts of stochastic choice. We provide two easily understood conditions each of which characterizes this representation: One condition generalizes the acyclicity condition used in revealed preference theory, and the other generalizes Luce's IIA condition. We relate the discrimination or selectivity of choice rules to properties of their associated perturbations, both across different agents and across decision problems. We also show that these representations correspond to a form of ambiguity‐averse preferences for an agent who is uncertain about her true utility.     

Subordinate Participation in Audit Budgeting Decisions: A Comparison of Decisions Influenced by Organizational Factors to Decisions Conforming with the Vroom-Jago Model*

This study examines the role of subordinate participation in the effectiveness of audit hours budget decisions in accounting firms. The study compares decisions influenced by organizational factors (such as organizational policies or the preferences of the superior) to decisions that conform to the Vroom-Jago (VJ) model. Our results indicate that actual level of participation used in budget decisions appears to be based primarily on perceived preferences of superiors and participation styles available under the circumstancesof the individual audit. However, results also indicate that decisions consistent with the Vroom-Jago model are characterized by higher decision quality and increased subordinatedevelopment. Since managers are apparently reluctant to use decision styles that conflictwith organizational factors, accounting firms may wish to gather information regarding the attributes of the decision context and use the VJ model to establish their available decision styles and determine the preferences of superiors. Doing so has the advantage of considering decision-specific attributes while enhancing the probability of manager compliance with a desired decision style.     

Uncertainty and Risk in Financial Markets

This paper considers a general equilibrium model in which the distinction between uncertainty and risk is formalized by assuming agents have incomplete preferences over state‐contingent consumption bundles, as in Bewley (1986). Without completeness, individual decision making depends on a set of probability distributions over the state space. A bundle is preferred to another if and only if it has larger expected utility for all probabilities in this set. When preferences are complete this set is a singleton, and the model reduces to standard expected utility. In this setting, we characterize Pareto optima and equilibria, and show that the presence of uncertainty generates robust indeterminacies in equilibrium prices and allocations for any specification of initial endowments. We derive comparative statics results linking the degree of uncertainty with changes in equilibria. Despite the presence of robust indeterminacies, we show that equilibrium prices and allocations vary continuously with underlying fundamentals. Equilibria in a standard risk economy are thus robust to adding small degrees of uncertainty. Finally, we give conditions under which some assets are not traded due to uncertainty aversion.     

Preference-Order Recursion for Finding Relevant Pure,Admissible and Optimal Statistical Decision Functions*

A preference-order recursion algorithm for obtaining a relevant subset of pure, admissible (non-dominated, efficient) decision functions which converges towards an optimal solution in statistical decision problems is proposed. The procedure permits a decision maker to interactively express strong binary preferences for partial decision functions at each stage of the recursion, from which an imprecise probability and/or utility function is imputed and used as one of several pruning mechanisms to obtain a reduced relevant subset of admissible decision functions or to converge on an optimal one. The computational and measurement burden is thereby mitigated significantly, for example, by not requiring explicit or full probability and utility information from the decision maker. The algorithm is applicable to both linear and nonlinear utility functions. The results of behavioral and computational experimentation show that the approach is viable, efficient, and robust.     

Distribution of Aggregate Utility Using Stochastic Elements of Additive Multiattribute Utility Models

Conventionally, elements of a multiattribute utility model characterizing a decision maker's preferences, such as attribute weights and attribute utilities, are treated as deterministic, which may be unrealistic because assessment of such elements can be imprecise and erroneous, or differ among a group of individuals. Moreover, attempting to make precise assessments can be time consuming and cognitively demanding. We propose to treat such elements as stochastic variables to account for inconsistency and imprecision in such assessments. Under these assumptions, we develop procedures for computing the probability distribution of aggregate utility for an additive multiattribute utility function (MAUF), based on the Edgeworth expansion. When the distributions of aggregate utility for all alternatives in a decision problem are known, stochastic dominance can then be invoked to filter inferior alternatives. We show that, under certain mild conditions, the aggregate utility distribution approaches normality as the number of attributes increases. Thus, only a few terms from the Edgeworth expansion with a standard normal density as the base function will be sufficient for approximating an aggregate utility distribution in practice. Moreover, the more symmetric the attribute utility distributions, the fewer the attributes to achieve normality. The Edgeworth expansion thus can provide a basis for a computationally viable approach for representing an aggregate utility distribution with imprecisely specified attribute weights and utilities assessments (or differing weights and utilities across individuals). Practical guidelines for using the Edgeworth approximation are given. The proposed methodology is illustrated using a vendor selection problem.     

Preferences for One‐Shot Resolution of Uncertainty and Allais‐Type Behavior

Experimental evidence suggests that individuals are more risk averse when they perceive risk that is gradually resolved over time. We address these findings by studying a decision maker who has recursive, nonexpected utility preferences over compound lotteries. The decision maker has preferences for one‐shot resolution of uncertainty if he always prefers any compound lottery to be resolved in a single stage. We establish an equivalence between dynamic preferences for one‐shot resolution of uncertainty and static preferences that are identified with commonly observed behavior in Allais‐type experiments. The implications of this equivalence on preferences over information systems are examined. We define the gradual resolution premium and demonstrate its magnifying effect when combined with the usual risk premium.     

Games and Mechanism Design in Machine Scheduling—An Introduction

We survey different models, techniques, and some recent results to tackle machine scheduling problems within a distributed setting. In traditional optimization, a central authority is asked to solve a (computationally hard) optimization problem. In contrast, in distributed settings there are several agents, possibly equipped with private information that is not publicly known, and these agents must interact to derive a solution to the problem. Usually the agents have their individual preferences, which induces them to behave strategically to manipulate the resulting solution. Nevertheless, one is often interested in the global performance of such systems. The analysis of such distributed settings requires techniques from classical optimization, game theory, and economic theory. The paper therefore briefly introduces the most important of the underlying concepts and gives a selection of typical research questions and recent results, focusing on applications to machine scheduling problems. This includes the study of the so‐called price of anarchy for settings where the agents do not possess private information, as well as the design and analysis of (truthful) mechanisms in settings where the agents do possess private information.     

Decisional Conflict and User Acceptance of Multicriteria Decision-Making Aids*

Despite the development of increasingly sophisticated and refined multicriteria decision-making (MCDM) methods, an examination of the experimental evidence indicates that users most often prefer relatively unsophisticated methods. In this paper, we synthesize theories and empirical findings from the psychology of judgment and choice to provide a new theoretical explanation for such user preferences. Our argument centers on the assertion that the MCDM method preferred by decision makers is a function of the degree to which the method tends to introduce decisional conflict. The model we develop relates response mode, decision strategy, and the salience of decisional conflict to user preferences among decision aids. We then show that the model is consistent with empirical results in MCDM studies. Next, the role of decisional conflict in problem formulation aids is briefly discussed. Finally, we outline future research needed to thoroughly test the theoretical mechanisms we have proposed.     

Entscheidungsunterstützung unter Berücksichtigung der Anforderungen von Entscheidungsträgern am Beispiel der Gestaltung von optionalen Girokonto-Tarifen

Quantitative decision models are used only if managers’ implementation conditions are met. Decision makers want tools that offer a set of good solutions so that they can evaluate different solutions according to various objectives without being forced to make their trade-offs explicit in a functional form. This also allows taking into account strategic aspects that cannot be modeled otherwise. In such situations, heuristics are needed which derive solutions from the structure and not so much from the mathematical properties. We present such a decision support tool for the problem of determining a menu of optional tariffs for checking accounts. The heuristic is based on the idea that for reasonably separable preferences across segments it is the best to offer for each segment the most preferred product. We use latent class choice-based conjoint analysis to estimate customer preferences and develop a customized choice-based conjoint design to take differences in individual demand into account. The proposed heuristic was used to support an actual decision problem for which the profit contribution has been increased substantially without having faced a considerable loss of customers.     

The Microeconomics of Efficient Group Behavior: Identification1

Consider a group consisting of S members facing a common budget constraint p'ξ=1: any demand vector belonging to the budget set can be (privately or publicly) consumed by the members. Although the intragroup decision process is not known, it is assumed to generate Pareto‐efficient outcomes; neither individual consumptions nor intragroup transfers are observable. The paper analyzes when, to what extent, and under which conditions it is possible to recover the underlying structure—individual preferences and the decision process—from the group's aggregate behavior. We show that the general version of the model is not identified. However, a simple exclusion assumption (whereby each member does not consume at least one good) is sufficient to guarantee generic identifiability of the welfare‐relevant structural concepts.     

基于Vidale-Wolfe模型的多市场广告预算分配决策模型

广告决策问题很长时间以来都是营销经理和学者们关注的热点。随着社会经济发展,越来越多的企业面对多个市场。如何在多个市场、广告总预算固定的状况下,合理分配各个市场广告预算以收到最优广告效果,是一个企业关心的较为重要的问题。经过比较,选择Vidale-Wolfe模型作为广告反应模型,在此基础上建立了多市场广告预算分配决策模型。考虑到一些营销策略对某些市场有特殊销售速率要求,该模型分为无特殊销售速率维持要求的多市场广告预算分配决策模型和有特殊销售速率维持要求的多市场广告预算分配决策模型两类,后者探讨了销售速率变化与达到指定销售速率两种要求下的广告预算最优分配问题,构建了优化模型,提出了模型参数取值与模型求解方法,最后给出了一个算例。     

Project Portfolio Selection: A Newsvendor Approach

We consider the problem of balancing the penalties associated with budgetary slack (being underbudget) and cost overruns in the project portfolio selection problem by addressing randomness in project costs and making individual project budgets decision variables. Setting the budget for a single project is shown to be analogous to the newsvendor problem. For related versions of the project portfolio selection problem we provide optimal and heuristic procedures. Numerical experiments are used to test the procedures and provide managerial guidelines. We show project budgets should be set so that each project in the portfolio has the same probability of running over budget, it is better to have a larger number of projects with less than ideal funding compared to a smaller number of projects with ideal funding, and substantial opportunities to select more projects with a higher expected profit are available if an aggregate portfolio budget is used.     

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).     

Keeping up with the Neighbors: Social Interaction in a Market Economy

We consider a world in which individuals have private endowments and trade in markets while their utility is negatively affected by the consumption of their neighbors. Our interest is in understanding how the social structure of comparisons, taken together with the familiar fundamentals of the economy (endowments, technology, and preferences), shapes equilibrium prices, allocations, and welfare. We show that equilibrium prices and consumption are a function of a single network statistic: centrality. An individual's “centrality” is given by the weighted sum of paths of different lengths to all others in a social network. In particular, prices are proportional to the sum of centralities, and an individual's consumption depends on how central she is relative to others in the network. Inequalities in wealth and connections reinforce each other in markets: A transfer of resources from less to more central agents raises prices. As segregated communities become integrated, the poor lose while the rich gain in utility! (JEL: D5, D6, D85)     

Risk Sharing in Private Information Models With Asset Accumulation: Explaining the Excess Smoothness of Consumption

We study testable implications for the dynamics of consumption and income of models in which first‐best allocations are not achieved because of a moral hazard problem with hidden saving. We show that in this environment, agents typically achieve more insurance than that obtained under self‐insurance with a single asset. Consumption allocations exhibit “excess smoothness,” as found and defined by Campbell and Deaton (1989). We argue that excess smoothness, in this context, is equivalent to a violation of the intertemporal budget constraint considered in a Bewley economy (with a single asset). We also show parameterizations of our model in which we can obtain a closed‐form solution for the efficient insurance contract and where the excess smoothness parameter has a structural interpretation in terms of the severity of the moral hazard problem. We present tests of excess smoothness, applied to U.K. microdata and constructed using techniques proposed by Hansen, Roberds, and Sargent (1991) to test the intertemporal budget constraint. Our theoretical model leads us to interpret them as tests of the market structure faced by economic agents. We also construct a test based on the dynamics of the cross‐sectional variances of consumption and income that is, in a precise sense, complementary to that based on Hansen, Roberds, and Sargent (1991) and that allows us to estimate the same structural parameter. The results we report are consistent with the implications of the model and are internally coherent.     

Strategyproof mechanism design for facility location games with weighted agents on a line

Approximation mechanism design without money was first studied in Procaccia and Tennenholtz (2009) by considering a facility location game. In general, a facility is being opened and the cost of an agent is measured by its distance to the facility. In order to achieve a good social cost, a mechanism selects the location of the facility based on the locations reported by agents. It motivates agents to strategically report their locations to get good outcomes for themselves. A mechanism is called strategyproof if no agents could manipulate to get a better outcome by telling lies regardless of any configuration of other agents. The main contribution in this paper is to explore the strategyproof mechanisms without money when agents are distinguishable. There are two main variations on the nature of agents. One is that agents prefer getting closer to the facility, while the other is that agents prefer being far away from the facility. We first consider the model that directly extends the model in Procaccia and Tennenholtz (2009). In particular, we consider the strategyproof mechanisms without money when agents are weighted. We show that the strategyproof mechanisms in the case of unweighted agents are still the best in the weighted cases. We establish tight lower and upper bounds for approximation ratios on the optimal social utility and the minimum utility when agents prefer to stay close to the facility. We then provide the lower and upper bounds on the optimal social utility and lower bound on the minimum distance per weight when agents prefer to stay far away from the facility. We also extend our study in a natural direction where two facilities must be built on a real line. Secondly, we propose an novel threshold based model to distinguish agents. In this model, we present a strategyproof mechanism that leads to optimal solutions in terms of social cost.     

Multi-time scale Markov decision process approach to strategic network growth of reverse supply chains

This paper addresses a complex set of decisions that surround the growth over time of reverse supply chain networks that collect used products for reuse, refurbishment, and/or recycling by processors. The collection network growth problem is decomposed into strategic, tactical and operational problems. This paper focuses on the strategic problem which is to determine how to allocate capital budget resource effectively to grow the network to meet long term collection targets and collection cost constraints. We model the strategic problem as a Markov decision process which can also be posed as multi-time scale Markov decision problem. The recruitment problem in a tactical level appears as a sub-problem for the strategic model. Using dynamic programming, linear programming and Q-Learning approaches, an heuristic is implemented to solve realistically sized problems. A numerical study demonstrates that the heuristic can obtain a good solution for the large-scale problem in reasonable time which is not possible when trying to obtain the optimal solution with the exact DP approach.     

Application of the knapsack model for budgeting

The budget problem of selecting projects (or activities) with known values (or payoffs) and associated costs, subject to a prescribed maximum budget, is akin to the knapsack problem, which is well documented in the literature. The optimal solution to maximise the total value of selected projects for a given budget constraint can readily be obtained. In practice, budgets are often somewhat flexible, or subject to possible changes, so that an optimal solution for a given budget value may not remain optimal when the budget is modified. It is, therefore, sensible in many situations to consider a budget range, instead of a single budget value. In addition to their original objective of maximising the total value of selected projects, decision makers are often concerned to get ‘value for money’, indicated by the ratio of payoff to cost. This paper examines how these questions can be tackled through the introduction of a stability index, to guide project selection within a defined budget range, and the use of a portfolio diagram, to help in the ranking of projects with respect to the stated twin objectives.     

Generalized symmetric weight assignment technique: Incorporating managerial preferences in data envelopment analysis using a penalty function

In this paper, we generalize the Symmetric Weight Assignment Technique to incorporate all managerial preferences in Data Envelopment Analysis (DEA). This is a method that promotes managerial preferences, while not changing the feasibility region of the nominal DEA model, unlike standard techniques such as cone ratio and assurance region that potentially yield infeasible problems. We discuss how this generalization is motivated by a real word problem where the decision maker's preference is not precisely known. We also discuss how we are using our generalization in solving a workforce allocation problem for the United States Navy.