Risk-averse Users Research Articles

Accounting for BEV Users’ Risk Attitudes and Charging Inertia in En Route Charging Choice Behavior

This paper innovatively explores BEV (battery electric vehicle) users’ risk attitudes and charging inertia, examining their effects on en route charging and charging route choice behavior. An attitudinal survey was conducted to explore the two latent variables of risk attitudes and charging inertia in relation to socioeconomic and travel-related characteristics. ICLV (Integrated choice and latent variable) models are adopted to estimate the latent variables and the charging choice behavior simultaneously. Specifically, uncertainty in energy consumption is first considered in the ICLV model, which is represented by the available range (AR) uncertainty. Multinomial logit (MNL) models directly incorporating socioeconomic attributes are employed as a reference for comparison with ICLV models. Results illustrate that risk attitudes and charging inertia both play significant roles in modeling en route charging choice behavior. Risk-averse users and users having charging inertia value AR uncertainty more. Battery range, charging frequency, and income emerge as the most crucial factors influencing users’ intention to charge en route. The results show significant heterogeneity of BEV users in attitudes and charging choice behavior, underscoring the importance of accounting for the heterogeneity in en route charging demand estimation and deployment optimization of public charging stations, particularly for medium-to long-distance trips.

Polysubstance use practices among women using anabolic-androgenic steroids (AAS)

BackgroundResearch with men who use anabolic-androgenic steroids (AAS) shows typologies exist where some younger and less risk-averse users engage in polysubstance use. Little research has investigated polysubstance use among women who use AAS. MethodThis study explored patterns of AAS and other illicit substance use among a sample of female AAS users involved in strength sports (e.g., bodybuilding) from Australia (n=7). The research also engaged in interviews with male AAS users who came into frequent contact with women using AAS either by coaching them or as peers (n=7). Data were analysed within a constructivist framework using thematic analysis. ResultsThe data suggests belonging to a female strength athlete identity may have pseudo-protective elements which results in reducing licit substance use, however, illicit substance use does not run counter to the culture and may be supported by it. DiscussionWomen who use AAS identified underlying factors, related to significant previous events in their lives, contributing to their polysubstance use. The male participants expressed similar views regarding underlying factors which contributed to women's use of other substances for recreational purposes. Further investigations are warranted to explore, more fully, the psychosocial factors which contribute to use of multiple illicit substances among women who use AAS and whether typologies exist.

Pricing Game of Smart Charging Services for Risk-Averse Users in the Smart Grid

Electric vehicles play a key role in the transition to an environmental-friendly transportation system and can meanwhile enhance the power system’s evolution to the smart grid. With the adoption of dynamic pricing and usage scheduling enabled by the smart grid equipment, a variety of smart charging strategies have been designed to make the most of flexibility contained in their considerable electricity demand, whereas less effort is devoted to users’ willingness to participate. In this paper, we model a noncooperative pricing game between two types of charging stations. One offers conventional fast charging and the other uses the electric vehicles’ onboard batteries to provide regulation service to the grid. With drivers’ risk attitudes and bounded rationality taken into consideration, we design a prospect theory-based decision model to calculate the proportion of users that would go for the regulation-providing charging option. The decision model of the customer base is a critical determinant of profitability and it enables two competitors to strategically set their prices that optimally balance between gaining in market share and growing in profit per client. We prove the existence of a pure strategy Nash equilibrium for the game proposed and compute the equilibrium prices in different circumstances with respect to market settings and user segments. A comprehensive analysis of the results gives insights into the key factors at play and provides the grid operators with indications of how to increase the penetration of electric vehicles in the ancillary service market.

“Price Tag” of Risk of Using E-Payment Service

In this research, the authors utilized a survey to evaluate the notional values of the overall risk, the privacy risk, and the financial risk of using a credit card and an RFID-based E-payment service from risk-neutral and risk-averse users. With the known extra financial risk (in terms of monetary value) to be faced by the users in using two different versions of an RFID-based E-payment service, the authors determined the notional monetary value of the extra privacy risk posed by providing personal and financial information to the E-payment service and the differences in the risk aversion of the two groups of users. The findings may help E-payment service developers design better E-payment services based on a better understanding of the value of personal data in their users’ perspectives and, thus, help determine the appropriate incentives for attracting users to use their services.

Insurance value of natural capital

Nature-based solutions to insurance are in high demand. We explore the idea that natural capital has an insurance value insofar as it can mitigate the effects of uncertainty on human well-being. We present a formal model that substantiates this claim. We propose a definition for the insurance value of natural capital for a stochastic and dynamic ecosystem that provides ecosystem services for a risk-averse user. The insurance value of natural capital depends on the properties of ecosystem dynamics as well as on the risk and time preferences of the ecosystem user. It can be positive or negative. We relate the natural insurance value to conservative use of the ecosystem and precautionary investment in the natural capital stock. For the case of logarithmic per-period utility we find that optimal management becomes more conservative with increasing uncertainty if and only if the insurance value of natural capital is positive. We qualify this finding for more general forms of the per-period utility function.

An investigation of route-choice in integrated public transport networks by risk-averse users

Globally, transport agencies are implementing integrated public transport systems to increase ridership. Transfers are a key component of such integrated systems; they facilitate connectivity among modes, allowing the system to function in unison. It is well known that transfers can cause users to feel anxious, due to the possibility of missed connections. The public transport network in Auckland, New Zealand, is undergoing a transformation into an integrated system, which means more routes with transfers are replacing direct routes. This study examines the route choice of public transport users when faced with multiple routes involving transfers. Four sub-models are developed to create the Route Choice Model. One of the contributions of the present study is the development of the Risk-Aversion sub-model, which provides a straight-forward representation of users’ risk profiles for route-choice associated with transfers. These four sub-models are applied to a proposed integrated public transport network to determine the ridership of the new routes involving transfers. The socio-economic characteristics included in this study are gender and age. The findings show that females are more risk-averse than male users, and that users aged 40 or over are more risk-averse than those under 40. Overall, users who are more risk-averse prefer the transfer options if the service is reliable, and the transfer waiting time is relatively short in proportion to the overall journey time. Future research is encouraged to investigate the effects of other socio-economic characteristics on users’ decisions to make transfers, using the findings to make further improvements to the network.

A consistent reliability-based user-equilibrium problem with risk-averse users and endogenous travel time correlations: Formulation and solution algorithm

The traditional traffic assignment model has been extended in the literature to incorporate uncertainty and travelers who are sensitive to it. However, the proposed formulations that model risk-averse users lack (i) a consistent representation of the various stochastic quantities involved and (ii) a general solution approach. In this context, this study formulates a consistent, reliability-based user-equilibrium problem with risk-averse travelers. In the proposed formulation, various stochastic quantities are consistent with each other: the stochastic origin–destination demands result in stochastic path-flows and in turn stochastic link-flows, which result in stochastic link travel times, and travelers make decisions based on the stochasticity of travel times. The formulation also incorporates (i) endogenous link-flow variances and covariances and (ii) flow-dependent and endogenous link travel time correlations. At equilibrium – which is defined over the distributions of travel times and flows – no user can improve her travel time reliability by unilaterally changing route. The conditions for existence of a solution to the formulated problem are presented. A gradient projection based algorithm is proposed to solve the formulated problem, which is demonstrated to be correct and efficient through computational experiments. We also show that ignoring consistency in the formulation can lead to potentially erroneous conclusions. Experiments also demonstrate that the solution can be sensitive to the demand levels, stochasticity in demand, and users’ degree of risk-aversion. This work has the potential to make existing reliability-based user-equilibrium formulations more general and operational. It also has important applications in reliability-based traffic planning and management.

Subjective-utility travel time budget modeling in the stochastic traffic network assignment

ABSTRACTIn this article, we propose a new model called subjective-utility travel time budget (SU-TTB) model to capture travelers' risk-averse route choices. In the travel time budget (TTB) and mean-excess travel time (METT) model, a predefined confidence level is needed to capture the risk-aversion in route choice. Due to the day-to-day route travel time variations, the exact confidence level is hard to be predicted. With the SU-TTB model, we assume travelers' confidence level belongs to an interval that they may comply with in the route choice. The two main components of SU-TTB are the utility function and the TTB model. We can show that the SU-TTB can be reduced to the TTB and METT model with proper utility function for the confidence levels. We can also prove its equivalence with our recently proposed nonlinear-expectation route travel time (NERTT) model in some cases and give some new interpretation on the NERTT with this equivalence. Finally, we formulate the SU-TTB model as a variational inequality (VI) problem to model the risk-averse user equilibrium (RAUE), termed as generalized RAUE (GRAUE). The GRAUE is solved via a heuristic gradient projection algorithm, and the model and solution algorithm are demonstrated with the Braess's traffic network and the Nguyen and Dupuis's traffic network.

Non-expected Route Choice Model under Risk on Stochastic Traffic Networks

In this paper, we propose a novel non-expected route travel time (NERTT) model, which belong to the rank-dependent expected utility model. The NERTT consists of two parts, which are the route travel time distribution and the distortion function. With the strictly increasing and strictly concave distortion function, we can prove that the route travel time in the proposed model is risk-averse, which is the main focus of this paper. We show two different reduction methods from the NERTT model to the travel time budget model and mean-excess travel time model. One method is based on the properly selected distortion functions and the other one is based on a general distortion function. Besides, the behavioral inconsistency of the expected utility model in the route choice can be overcome with the proposed model. The NERTT model can also be generalized to the non-expected disutility (NED) model, and some relationship between the NED model and the route choice model based on the cumulative prospect theory can be shown. This indicates that the proposed model has some generality. Finally, we develop a non-expected risk-averse user equilibrium model and formulate it as a variational inequality (VI) problem. A heuristic gradient projection algorithm with column generation is used to solve the VI. The proposed model and algorithm are tested on some hypothetical traffic networks and on some large-scale traffic networks.

Opting Out of Incentive Mechanisms: A Study of Security as a Non-Excludable Public Good

In a network of interdependent users, the expenditure in security measures by an entity affects not only herself, but also other users interacting with her. As a result, users’ efforts toward security can be viewed as a public good; the optimal provision of which in a system of self-interested entities requires the design of appropriate incentives through an external mechanism. In this paper, we propose the notion of exit equilibrium to study users’ voluntary participation in such incentive mechanisms. We show a fundamental result that, due to the non-excludable nature of security, there exists no reliable mechanism, which can incentivize socially optimal investments, while ensuring voluntary participation and maintaining a weakly balanced budget, for all instances of security games. To further illustrate this result, we analyze the performance of two well-known incentive mechanisms, namely the Pivotal (VCG) and Externality mechanisms, in security games. We illustrate how, given a mechanism, stable coalitions of participating users may emerge, leading to an improved, yet sub-optimal security status. We further extend the impossibility result to risk-averse users, and discuss its implications on the viability of using cyber-insurance contracts to improve the state of cyber security.

A Mean-Risk Model for the Traffic Assignment Problem with Stochastic Travel Times

Heavy and uncertain traffic conditions exacerbate the commuting experience of millions of people across the globe. When planning important trips, commuters typically add an extra buffer to the expected trip duration to ensure on-time arrival. Motivated by this, we propose a new traffic assignment model that takes into account the stochastic nature of travel times. Our model extends the traditional model of Wardrop competition when uncertainty is present in the network. The focus is on strategic risk-averse users who capture the trade-off between travel times and their variability in a mean-standard deviation objective, defined as the mean travel time plus a risk-aversion factor times the standard deviation of travel time along a path. We consider both infinitesimal users, leading to a nonatomic game, and atomic users, leading to a discrete finite game. We establish conditions that characterize an equilibrium traffic assignment and find when it exists. The main challenge is posed by the users' risk aversion, since the mean-standard deviation objective is nonconvex and nonseparable, meaning that a path cannot be split as a sum of edge costs. As a result, even an individual user's subproblem—a stochastic shortest path problem—is a nonconvex optimization problem for which no polynomial time algorithms are known. In turn, the mathematical structure of the traffic assignment model with stochastic travel times is fundamentally different from the deterministic counterpart. In particular, an equilibrium characterization requires exponentially many variables, one for each path in the network, since an edge flow has multiple possible path-flow decompositions that are not equivalent. Because of this, characterizing the equilibrium and the socially optimal assignment, which minimizes the total user cost, is more challenging than in the traditional deterministic setting. Nevertheless, we prove that both can be encoded by a representation with just polynomially many paths. Finally, under the assumption that the standard deviations of travel times are independent from edge loads, we show that the worst-case ratio between the social cost of an equilibrium and that of an optimal solution is not higher than the analogous ratio in the deterministic setting. In other words, uncertainty does not further degrade the system performance in addition to strategic user behavior alone.

Should WADA remove the illicit drugs from the prohibited list?

Research with men who use anabolic-androgenic steroids (AAS) shows typologies exist where some younger and less risk-averse users engage in polysubstance use. Little research has investigated polysubstance use among women who use AAS.This study explored patterns of AAS and other illicit substance use among a sample of female AAS users involved in strength sports (e.g., bodybuilding) from Australia (n=7). The research also engaged in interviews with male AAS users who came into frequent contact with women using AAS either by coaching them or as peers (n=7). Data were analysed within a constructivist framework using thematic analysis.The data suggests belonging to a female strength athlete identity may have pseudo-protective elements which results in reducing licit substance use, however, illicit substance use does not run counter to the culture and may be supported by it.Women who use AAS identified underlying factors, related to significant previous events in their lives, contributing to their polysubstance use. The male participants expressed similar views regarding underlying factors which contributed to women's use of other substances for recreational purposes. Further investigations are warranted to explore, more fully, the psychosocial factors which contribute to use of multiple illicit substances among women who use AAS and whether typologies exist.

A Mean-Risk Model for the Traffic Assignment Problem with Stochastic Travel Times

Heavy and uncertain traffic conditions exacerbate the commuting experience of millions of people across the globe. When planning important trips, commuters typically add an extra buffer to the expected trip duration to ensure on-time arrival. Motivated by this, we propose a new traffic assignment model that takes into account the stochastic nature of travel times. Our model extends the traditional model of Wardrop competition when uncertainty is present in the network. The focus is on strategic risk-averse users who capture the tradeoff between travel times and their variability in a mean-standard deviation (mean-stdev) objective, defined as the mean travel time plus a risk-aversion factor times the standard deviation of travel time along a path. We consider both infinitesimal users, leading to a non-atomic game, and atomic users, leading to a discrete finite game.We establish conditions that characterize an equilibrium traffic assignment and find when it exists. The main challenge is posed by the users’ risk aversion, since the mean-stdev objective is non-convex and non-separable, meaning that a path cannot be split as a sum of edge costs. As a result, even an individual user’s sub-problem — a stochastic shortest path problem — is a non-convex optimization problem for which no polynomial time algorithms are known. In turn, the mathematical structure of the traffic assignment model with stochastic travel times is fundamentally different from the deterministic counterpart. In particular, an equilibrium characterization requires exponentially many variables, one for each path in the network, since an edge-flow has multiple possible path-flow decompositions that are not equivalent. Because of this, characterizing the equilibrium and the socially-optimal assignment, which minimizes the total user cost, is more challenging than in the traditional deterministic setting. Nevertheless, we prove that both can be encoded by a representation with just polynomially-many paths. Finally, for the case of uncertainty parameters that are independent from edge loads, we show that although an equilibrium assignment results in a total user cost that is higher than that of the socially-optimal one, it is not higher than the analogous ratio in the deterministic setting. In other words, uncertainty does not further degrade the system performance in addition to strategic user behavior alone.

Economic Interpretation of Probabilities Estimated by Maximum Likelihood or Score

The conventional method of estimating a probability prediction model by maximum likelihood (MLE) is a form of maximum score estimation with economic meaning. Of all the probabilities that a given model might have produced, those obtained by MLE yield maximum in-sample betting return to a log utility investor. Recognition of this affinity between MLE and log utility begs the wider methodological question of whether different decision makers benefit in different degrees from different probabilities. Probabilities produced by MLE can be either too conservative or too bold relative to those found by maximizing utility under more risk-tolerant or risk-averse score functions. A very (not very) risk-averse user, who bets characteristically small (large) fractions of wealth based on a conservative forecast, is bound to make a rapidly (slowly) increasing bet as the forecast probability becomes progressively bolder or more distant from the market probability. The effect of this interaction between risk aversion and forecast is that a highly risk-averse user may need a much bolder forecast to obtain the same certainty equivalent as a more risk-tolerant investor. It follows more broadly that professional forecasters should anticipate how a client with given risk aversion expects to gain from any given forecast, or forecast revision, before committing resources toward making a better informed (but still honest) forecast. This paper was accepted by Peter Wakker, decision analysis.

Management Insights

Management Insights

Wardrop Equilibria with Risk-Averse Users

Network games can be used to model competitive situations in which agents select routes to minimize their cost. Common applications include traffic, telecommunication and distribution networks. Although traditional network models have assumed that realized costs only depend on congestion, in most applications they also have an uncertain component. We extend Wardrop’s network game (1952) by adding random deviations, which are independent of the flow, to the cost functions that model congestion in each arc. We map these uncertainties into a Wardrop equilibrium model with nonadditive path costs. The cost on a path is given by the sum of the congestion on its arcs plus a constant safety margin determined by risk-averse agents. First, we prove that an equilibrium for this game always exists and is essentially unique. Then, we introduce three specific equilibrium models that fall within this framework: the percentile equilibrium where agents select paths that minimize a specified percentile of the uncertain cost; the added-variability equilibrium where agents add a multiple of the variability of the cost of each arc to the expected cost; and the robust equilibrium where agents select paths by solving a robust optimization problem that imposes a limit on the number of arcs that can deviate from the mean. The percentile equilibrium is difficult to compute because minimizing a percentile among all paths is computationally hard. Instead, the added-variability and robust Wardrop equilibria can be computed efficiently in practice: the former reduces to a standard Wardrop equilibrium problem and the latter is found using a column generation approach that repeatedly solves robust shortest path problems, which are polynomially solvable. Through computational experiments of some random and some realistic instances, we explore the benefits and trade-offs of the proposed solution concepts. We show that when agents are risk averse, both the robust and added-variability equilibria better approximate percentile equilibria than the classic Wardrop equilibrium.

Wardrop Equilibria with Risk-Averse Users

Network games can be used to model competitive situations in which agents select routes to minimize their cost. Common applications include traffic, telecommunication, and distribution networks. Although traditional network models have assumed that realized costs only depend on congestion, in most applications they also have an uncertain component. We extend the traffic assignment problem first proposed by Wardrop in 1952 by adding random deviations, which are independent of the flow, to the cost functions that model congestion in each arc. We map these uncertainties into a Wardrop equilibrium model with nonadditive path costs. The cost on a path is given by the sum of the congestion on its arcs plus a constant safety margin that represents the agents' risk aversion. First, we prove that an equilibrium for this game always exists and is essentially unique. Then, we introduce three specific equilibrium models that fall within this framework: the percentile equilibrium where agents select paths that minimize a specified percentile of the uncertain cost; the added-variability equilibrium where agents add a multiple of the variability of the cost of each arc to the expected cost; and the robust equilibrium where agents select paths by solving a robust optimization problem that imposes a limit on the number of arcs that can deviate from the mean. The percentile equilibrium is difficult to compute because minimizing a percentile among all paths is computationally hard. Instead, the added-variability and robust Wardrop equilibria can be computed efficiently in practice: The former reduces to a standard Wardrop equilibrium problem and the latter is found using a column generation approach that repeatedly solves robust shortest path problems, which are polynomially solvable. Through computational experiments of some random and some realistic instances, we explore the benefits and trade-offs of the proposed solution concepts. We show that when agents are risk averse, both the robust and added-variability equilibria better approximate percentile equilibria than the classic Wardrop equilibrium.

The Private and Public Insurance Value of Conservative Biodiversity Management

The ecological literature suggests that biodiversity reduces the variance of ecosystem services. Thus, conservative biodiversity management has an insurance value to risk-averse users of ecosystem services. We analyze a conceptual ecological-economic model in which such management measures generate a private benefit and, via ecosystem processes at higher hierarchical levels, a positive externality on other ecosystem users. We find that ecosystem management and environmental policy depend on the extent of uncertainty and risk-aversion as follows: (i) Individual effort to improve ecosystem quality unambiguously increases. The free-rider problem may decrease or increase, depending on the characteristics of the ecosystem and its management; in particular, (ii) the size of the externality may decrease or increase, depending on how individual and aggregate management effort influence biodiversity; and (iii) the welfare loss due to free-riding may decrease or increase, depending on how biodiversity influences ecosystem service provision.

Auctioning resources in Grids: model and protocols

In this paper, we propose and study an auction model for resource management in Grids. We propose and investigate by simulation three types of auction-based resource-allocation protocols: (i) first-price auction protocol; (ii) Vickrey auction protocol; and (iii) double auction protocol. The goal is to find which of these is best suited to the Grid environment from the users' perspective as well as from the resources' perspective. The results showed that when we consider a mix of risk-averse and risk-neutral users, the first-price auction protocol favors resources while the Vickrey auction protocol favors users. On the other hand, the double auction protocol favors both users and resources. Copyright © 2006 John Wiley & Sons, Ltd.

Risk-averse user equilibrium traffic assignment: an application of game theory

Transport network users frequently have to make route choices in the presence of uncertainty about route costs. Uncertainty about costs differs from variation in cost perception, since uncertainty requires network users to have a strategy toward risk. The conventional approach is to add a safety margin based on the standard deviation of link cost. However, this requires the specification of the cost distribution. An alternative approach is presented here whereby the network user “plays through” all the possible eventualities before selecting his best route. A deterministic user equilibrium traffic assignment is shown to be equivalent to the mixed-strategy Nash equilibrium of an n-player, non-cooperative game. Then an n+ m-player, non-cooperative game is formulated, where n network users seek their best routes and m origin–destination (OD)-specific demons penalise the network users maximally by failing links. The mixed-strategy Nash equilibrium of this game is shown to describe a risk-averse user equilibrium traffic assignment. A simple solution procedure is presented, along with an illustrative example.