This article introduces a new method for eliciting prior distributions from experts. The method models an expert decision-making process to infer a prior probability distribution for a rare event A. More specifically, assuming there exists a decision-making process closely related to A which forms a decision Y, where a history of decisions have been collected. By modelling the data observed to make the historic decisions, using a Bayesian model, an analyst can infer a distribution for the parameters of the random variable Y. This distribution can be used to approximate the prior distribution for the parameters of the random variable for event A. This method is novel in the field of prior elicitation and has the potential of improving upon current methods by using real-life decision-making processes, that can carry real-life consequences, and, because it does not require an expert to have statistical knowledge. Future decision making can be improved upon using this method, as it highlights variables that are impacting the decision making process. An application for eliciting a prior distribution of recidivism, for an individual, is used to explain this method further.
We consider a variant of the hide-and-seek game in which a seeker inspects multiple hiding locations to find multiple items hidden by a hider. Each hiding location has a maximum hiding capacity and a probability of detecting its hidden items when an inspection by the seeker takes place. The objective of the seeker (resp. hider) is to minimize (resp. maximize) the expected number of undetected items. This model is motivated by strategic inspection problems, where a security agency is tasked with coordinating multiple inspection resources to detect and seize illegal commodities hidden by a criminal organization. To solve this large-scale zero-sum game, we leverage its structure and show that its mixed strategies Nash equilibria can be characterized using their unidimensional marginal distributions, which are Nash equilibria of a lower dimensional continuous zero-sum game. This leads to a two-step approach for efficiently solving our hide-and-seek game: First, we analytically solve the continuous game and compute the equilibrium marginal distributions. Second, we derive a combinatorial algorithm to coordinate the players' resources and compute equilibrium mixed strategies that satisfy the marginal distributions. We show that this solution approach computes a Nash equilibrium of the hide-and-seek game in quadratic time with linear support. Our analysis reveals a complex interplay between the game parameters and allows us to evaluate their impact on the players' behaviors in equilibrium and the criticality of each location.
Benefit–cost analyses are critical to support U.S. agencies’ programmatic decision making. These analyses are particularly challenging when one of the benefits is adversary deterrence. This paper presents a framework for calculating the value of deterrence related to countermeasures implemented to mitigate an attack by an adaptive adversary. We offer an approach for partitioning the benefit of countermeasures into three components: (1) threat reduction (deterrence), (2) vulnerability reduction, and (3) consequence mitigation. The benefit of a countermeasure is measured by the expected value of countermeasure implementation (EVCI) attributable to a specific countermeasure. It is based on the concept of expected value of imperfect control, defined as the difference in the expected values of alternatives with and without countermeasures. The EVCI represents all the benefits of implementing the countermeasure and is derived from three sources: (1) changes in attack probability (threat reduction from deterrence), (2) changes in detection probability (vulnerability reduction), and (3) changes in the distribution of attack outcomes (consequence mitigation). We partition the EVCI and estimate the portion attributable to each of these three sources to quantify the unique benefit of each. We provide two applications of the partitioning methodology using examples from the published literature that examine countermeasures designed to protect commercial aircraft against man-portable air defense systems. The proposed framework provides an approach for explicitly accounting separately for deterrence, vulnerability reduction, and consequence mitigation in benefit–cost analyses. It provides quantifiable insights into how countermeasures reduce terrorism risk. Funding: This material is based upon work supported by the U.S. Department of Homeland Security under [Grant Award 22STESE00001-02-00]. The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of the U.S. Department of Homeland Security. This award was made to Northeastern University and the University of Southern California is a sub-awardee. This work was also supported by the National Science Foundation [Grant 2027296] awarded to Decision Research.
Limited information, time, or capacity may prevent customers from acting as utility maximizers when making purchase decisions. Rather, they would settle for a good enough option; that is, they stop searching and make a purchase as soon as they find an acceptable alternative. We incorporate this behavior in an assortment-optimization problem. Whereas different approaches to modeling customer choice are adopted in assortment planning, all assume customers are utility maximizers. Our work bridges the research streams of assortment planning and bounded rationality, particularly satisficing behavior. In addition, we define a limit for the search budget of customers, in which customers leave without purchase after examining a certain number of items. This assumption brings a new perspective to the assortment-planning literature, enabling us to capture the choice-overload effect. We prove that the firm’s problem of finding the optimal assortment is NP-hard. We further establish certain structural properties of the optimal decision, which allows us to reformulate the model as a mixed-integer program. We analytically derive a tight upper bound on the percentage loss in the firm’s expected profit for small instances when it assumes incorrectly that customers are utility maximizers. For larger instances, we take a numerical approach to determine the loss. Our results indicate that firms offering low-involvement products, among those dealing with satisficing customers, are more likely to face substantial profit loss if they ignore this behavior. Supplemental Material: The e-companion is available at https://doi.org/10.1287/deca.2022.0063 .
Noise traders are a central idea in the modern theory of asset markets, yet there is not a standard model of such agents in contrast to the well-established representation of rational agents as expected utility maximizers. We propose the Hurwicz criterion, a classical criterion in decision analysis for choice under uncertainty, as a foundation for noise traders in asset markets. Hurwicz agents trade on optimism and pessimism and do not trade on information. A binary asset market is introduced with asymmetric information and heterogeneity both in rationality and in ambiguity attitudes. In this environment, noise trader behavior is endogenously positively correlated, the market is more efficient in low sentiment periods, and the favorite-longshot bias holds in equilibrium. The analysis demonstrates that aggregate market properties such as positive trading volume and the favorite longshot bias can be derived from the micro behavior of individual agents that have an axiomatic foundation.
