Stochastic Dominance: An Approach to Decision Making Under Risk

This paper introduces stochastic dominance as a technique to reduce the set of possible actions that a decision maker must consider in a decision problem under risk. The procedure usually does not choose an optimal action, but instead eliminates certain actions as unacceptable. Very little need be known about the decision maker's utility function. Two possible applications are presented: upgrading buildings to better withstand an earthquake; and choosing a site for a LNG facility.     

Bounded Memory and Biases in Information Processing

Before choosing among two actions with state‐dependent payoffs, a Bayesian decision‐maker with a finite memory sees a sequence of informative signals, ending each period with fixed chance. He summarizes information observed with a finite‐state automaton. I characterize the optimal protocol as an equilibrium of a dynamic game of imperfect recall; a new player runs each memory state each period. Players act as if maximizing expected payoffs in a common finite action decision problem. I characterize equilibrium play with many multinomial signals. The optimal protocol rationalizes many behavioral phenomena, like “stickiness,” salience, confirmation bias, and belief polarization.     

基于有限合作机制的群决策熵模型研究

研究一类具有合作机制的群决策问题。提出两阈值的合作函数对决策人之间的合作关系进行模糊分类,采用模糊测度方法度量决策人和决策人集的权力指数,建立合作群决策的非线性规划熵模型集结权力指数,并基于极大熵的最优化原理求解该模型。利用Choquet模糊积分计算备选方案的综合评价值,并对备选方案排序选择最优方案。最后通过算例分析并验证合作群决策模型和运用模糊积分方法求解模型的合理性、有效性。     

基于理想决策单元参照求解策略的DEA交叉效率评价模型

在已有关于DEA交叉效率评价模型中,激进型模型和仁慈型模型会因评价结果不一致而导致实际应用中难以对它们予以抉择的难题;中立型模型虽在形式上规避了前述问题,但其本身存在着理论偏差。针对上述问题,基于TOPSIS的理想点构造方法,提出了一种关于DEA交叉效率评价的新模型,即基于理想决策单元参照求解策略的DEA交叉效率评价模型。该模型不仅具有理论的严谨性,可以规避激进型模型与仁慈型模型之间的选择难题,而且相对于它们而言能够更好地坚持DEA最有利于被评价决策单元的基本思想。数值模拟分析表明新模型具有解决实际问题的较好适用性。     

考虑决策者后悔规避的风险投资项目选择方法

在风险投资项目选择过程中,决策者通常是有限理性的,会尽量避免选择可能会令其感到后悔的风险投资项目,而在涉及多个行业的风险投资项目选择过程中如何考虑决策者后悔规避的心理行为因素,这方面的研究特别需要关注。本文提出了一种涉及多个行业的考虑决策者后悔规避的风险投资项目选择方法。在该方法中,首先计算各风险投资项目在不同市场状态下的项目价值;然后,计算各组合市场状态发生的概率;进一步地,构建后悔函数刻画决策者后悔的心理感知,并通过计算不同行业的各风险投资项目的综合效用值得到风险投资项目的排序结果。最后,通过一个算例说明了本文提出方法的可行性与有效性。     

基于贝叶斯网络推理的双重不确定信息集结模型

针对一类不确定多属性决策问题,提出了基于贝叶斯网络推理的信息集结决策模型。根据决策依据信息,建立了决策方案综合属性值优劣的范围估计模型;由影响方案属性的因素构成的贝叶斯网络拓扑结构图,建立了基于贝叶斯推理的方案综合属性值确定模型;基于两类信息的内在关联性,提出了两种结果集结的最大相似度模型,最后得出方案综合属性值,算例表明基于贝叶斯网络推理的双重不确定信息集结模型是有效的。     

Sequential Search and Selection Problem Under Uncertainty

This paper formulates and discusses a series of sequential decision problems of the following common structure: A decision alternative of multiple attributes‐that is, a job, an employee, or an investment alternative‐is to be selected within a certain fixed length of time. An unknown number of alternatives are presented sequentially, either deterministically or in a random manner. The decision maker can rank all the alternatives from best to worst without ties, and the decision to accept or reject an alternative is based solely on the relative ranks of those alternatives evaluated so far. The nonparametric sequential decision problem is first studied for a model involving a discrete time period and then generalized in terms of continuous time. Also considered is a variant of this problem involving a Bayesian estimation of (1) the uncertain probability of having an alternative at a given stage in the discrete‐time model and (2) the arrival rate of alternatives in the continuous‐time model. The optimal selection strategy that maximizes the probability of selecting the absolute best alternative is illustrated with the job search problem and the single‐machine job assignment problem.     

A Note on Comparative Ambiguity Aversion and Justifiability

We consider a decision maker who ranks actions according to the smooth ambiguity criterion of Klibanoff, Marinacci, and Mukerji (2005). An action is justifiable if it is a best reply to some belief over probabilistic models. We show that higher ambiguity aversion expands the set of justifiable actions. A similar result holds for risk aversion. Our results follow from a generalization of the duality lemma of Wald (1949) and Pearce (1984).     

基于修正Russell方法的模糊决策单元的排序

文章首先建立基于修正Russell方法的超效率DEA模型,然后基于模糊数的比较,建立并求解模糊环境下的基于修正Russell方法的超效率DEA模型,从而解决了模糊决策单元的全排序问题。文末的算例将基于修正Russell方法的模糊超效率DEA模型,与基于CCR模型的模糊超效率DEA模型的结果进行了比较分析。     

A statistical framework for strategic decision making with AHP: Probability assessment and Bayesian revision

A probability assessment framework is outlined for an organizational decision involving a conditioning event (CE). The decision may, for example, involve a new-product launch (strategic decision) dependent on the outcome of market research (CE). The framework illustrates how Bayesian revision could be employed as related “news” arrives intermittently to revise current probabilities prior to decision implementation. A unique contribution of this paper is its utilization of the analytic hierarchy process to ascertain a set of consistent and coherent probabilities for the event/sample spaces at all stages of the decision process.     

Decision Making for Risk Management: A Comparison of Graphical Methods for Presenting Quantitative Uncertainty

Previous research has shown that people err when making decisions aided by probability information. Surprisingly, there has been little exploration into the accuracy of decisions made based on many commonly used probabilistic display methods. Two experiments examined the ability of a comprehensive set of such methods to effectively communicate critical information to a decision maker and influence confidence in decision making. The second experiment investigated the performance of these methods under time pressure, a situational factor known to exacerbate judgmental errors. Ten commonly used graphical display methods were randomly assigned to participants. Across eight scenarios in which a probabilistic outcome was described, participants were asked questions regarding graph interpretation (e.g., mean) and made behavioral choices (i.e., act; do not act) based on the provided information indicated that decision‐maker accuracy differed by graphical method; error bars and boxplots led to greatest mean estimation and behavioral choice accuracy whereas complementary cumulative probability distribution functions were associated with the highest probability estimation accuracy. Under time pressure, participant performance decreased when making behavioral choices.     

On the Rank-Based Selection Strategy for the Group Interview Problem*

For the so-called group interview problem in which several groups of choice alternatives are presented sequentially to the decision maker, the optimal selection strategy is derived that minimizes the expected rank of the selected choice or purchased product. For the case in which the sequence of groups can be rearranged by the decision maker, a simple heuristic procedure is proposed for obtaining a near-optimal sequence of groups, and the performance of the heuristic procedure in a Monte Carlo simulation is accessed. According to the heuristic procedure, the consumer is advised to visit smaller stores first and then move to larger stores later to increase the likelihood of finding a better product. Finally, the optimal selection strategy and the heuristic procedure are compared with those proposed by Chun, Moskowitz, and Plante (1993) and the problem of locating a new store in an area where there are several competing stores is discussed. The optimal selection strategy and the heuristic procedure can be applied to many sequential decision problems such as the consumer search and purchase process.     

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.     

Strict Uncertainty: A Criterion for Moderately Pessimistic Decision Makers*

This paper proposes a decision rule to rank actions under strict uncertainty, the available information being limited to the states of nature, the set of alternative rows, and the consequence of choosing every row if a given state occurs. This rule is suitable to moderately pessimistic individuals and social groups, these agents being neither maximax nor maximin decision makers but people who assume that the best outcome from the action will not occur. For these decision makers the paper shows the existence of a consistent weight system in which one and only one weight is attached to each state of the world under plausible conditions of domination. Most of the traditional axioms are satisfied by the proposed ranking approach. In the frame of disappointment (measured by ranges of column dispersion), the meaning of some controversial postulates used in the literature is explained. The proposed criterion is a departure from Laplace's (1825) rule and from the remaining standard criteria. Only in the special case of equal column dispersion do both Laplace's rule and the proposed weights lead to the same solution.     

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.     

风险规避型供应链的收益共享机制研究

探讨了由风险规避型零售商与风险规避型供应商组成的两级供应链协作激励问题.首先研究了Stackelberg主从对策模型下风险规避型零售商与风险规避型供应商的决策行为,并分析了双方的风险规避系数对双方决策行为的影响.然后,研究了垂直一体化模型下风险规避型供应链的决策行为,同样分析了双方风险规避系数对供应链决策行为的影响程度.最后,提出采用收益共享契约机制来协调该供应链.并通过数值实验进一步分析供应商与零售商的风险规避系数对双方的决策行为及收益共享系数的影响程度.     

Quantitative Comparison of Approximate Solution Sets for Bi‐criteria Optimization Problems*

We present the Integrated Preference Functional (IPF) for comparing the quality of proposed sets of near‐pareto‐optimal solutions to bi‐criteria optimization problems. Evaluating the quality of such solution sets is one of the key issues in developing and comparing heuristics for multiple objective combinatorial optimization problems. The IPF is a set functional that, given a weight density function provided by a decision maker and a discrete set of solutions for a particular problem, assigns a numerical value to that solution set. This value can be used to compare the quality of different sets of solutions, and therefore provides a robust, quantitative approach for comparing different heuristic, a posteriori solution procedures for difficult multiple objective optimization problems. We provide specific examples of decision maker preference functions and illustrate the calculation of the resulting IPF for specific solution sets and a simple family of combined objectives.     

Using Real‐Time Decision Tools to Improve Distributed Decision‐Making Capabilities in High‐Magnitude Crisis Situations*

Multi‐organizational collaborative decision making in high‐magnitude crisis situations requires real‐time information sharing and dynamic modeling for effective response. Information technology (IT) based decision support tools can play a key role in facilitating such effective response. We explore one promising class of decision support tools based on machine learning, known as support vector machines (SVM), which have the capability to dynamically model and analyze decision processes. To examine this capability, we use a case study with a design science approach to evaluate improved decision‐making effectiveness of an SVM algorithm in an agent‐based simulation experimental environment. Testing and evaluation of real‐time decision support tools in simulated environments provides an opportunity to assess their value under various dynamic conditions. Decision making in high‐magnitude crisis situations involves multiple different patterns of behavior, requiring the development, application, and evaluation of different models. Therefore, we employ a multistage linear support vector machine (MLSVM) algorithm that permits partitioning decision maker response into behavioral subsets, which can then individually model and examine their diverse patterns of response behavior. The results of our case study indicate that our MLSVM is clearly superior to both single stage SVMs and traditional approaches such as linear and quadratic discriminant analysis for understanding and predicting behavior. We conclude that machine learning algorithms show promise for quickly assessing response strategy behavior and for providing the capability to share information with decision makers in multi‐organizational collaborative environments, thus supporting more effective decision making in such contexts.     

Incorporating preference information in interactive reference point methods for multiobjective optimization

In this paper, we introduce new ways of utilizing preference information specified by the decision maker in interactive reference point based methods. A reference point consists of desirable values for each objective function. The idea is to take the desires of the decision maker into account more closely when projecting the reference point onto the set of nondominated solutions. In this way we can support the decision maker in finding the most satisfactory solutions faster. In practice, we adjust the weights in the achievement scalarizing function that projects the reference point. We identify different cases depending on the amount of additional information available and demonstrate the cases with examples. Finally, we summarize results of extensive computational tests that give evidence of the efficiency of the ideas proposed.