Prospect Theory Parameters Research Articles

Research on Chaotic Characteristics of Cascade Failure in Rail Transit Networks considering Nonlinear Load Fluctuations

The stable and efficient operation of rail transit networks (RTNs) is critical for the integrated development of metropolitan areas. However, numerous studies have indicated that RTNs are prone to large‐scale cascading failures when subjected to disturbances. To address the limitations of traditional cascading failure models, this paper proposes an innovative cascading failure model for metropolitan areas RTNs, which incorporates nonlinear load fluctuations and the bounded rationality of passengers. This model aims to capture the cascading failure characteristics of RTNs with chaotic properties under 12 combination strategies. A single‐ and dual‐parameter coupling analysis of chaotic evolution parameters and prospect theory parameters are conducted. Taking the RTN in the Chengdu metropolitan area as an example, both the static characteristics and cascading failure features of the network are analyzed. The findings reveal the following: (i) the RTN is a assortativity network and lacks small‐world and scale‐free properties. (ii) During network disturbances, a higher level of passenger familiarity with the network increases the likelihood of large‐scale cascading failures. (iii) When passengers tend to avoid risks, stations with higher carrying capacity are more prone to failures. This study holds significant implications for ensuring the stable and reliable operation of rail transit systems within metropolitan areas.

Risky business: Effects of stress on risky decision making

Decision-making under risk differs for potential gains compared to potential losses. The discrepancy in how gains and losses are assessed is best described by cumulative prospect theory, which postulates that individual risk attitude is more risk seeking in the face of potential losses (i.e., gambling to avoid a loss), more risk averse in the face of potential gains (i.e., opting for a smaller, more secure payout), and more likely to overweight low-probability events (e.g., buying a lottery ticket). Stress is known to modulate decision-making; however, how stress affects individual parameters of risk attitude remains unclear. Participants randomly assigned to the stress condition completed a Zoom-adapted Trier Social Stress Test, and those assigned to the control condition completed a corresponding control task. Participants then completed a task designed to estimate cumulative prospect theory parameters of risky decision-making through a series of gambles. Bayesian hierarchical modeling was used to estimate individual preferences for risk aversion, loss aversion, and probability distortion. Stressed participants exhibited less risk averse behaviors than control participants, with their behavior approaching risk-neutral, p=0.019. Additionally, stressed participants had increased probability distortion than control participants, indicating more overweighting of extreme events, p=.005 Stressed participants were also less loss averse than control participants, p<.001. We found that stress altered risk attitudes by altering risk aversion, probability distortion, and loss aversion. By understanding which domains of risk attitude are altered by stress, better therapeutic practices can be developed to aid individuals make better decisions while under stress.

Reliability of Decision-Making and Reinforcement Learning Computational Parameters.

Computational models can offer mechanistic insight into cognition and therefore have the potential to transform our understanding of psychiatric disorders and their treatment. For translational efforts to be successful, it is imperative that computational measures capture individual characteristics reliably. Here we examine the reliability of reinforcement learning and economic models derived from two commonly used tasks. Healthy individuals (N = 50) completed a restless four-armed bandit and a calibrated gambling task twice, two weeks apart. Reward and punishment learning rates from the reinforcement learning model showed good reliability and reward and punishment sensitivity from the same model had fair reliability; while risk aversion and loss aversion parameters from a prospect theory model exhibited good and excellent reliability, respectively. Both models were further able to predict future behaviour above chance within individuals. This prediction was better when based on participants' own model parameters than other participants' parameter estimates. These results suggest that reinforcement learning, and particularly prospect theory parameters, as derived from a restless four-armed bandit and a calibrated gambling task, can be measured reliably to assess learning and decision-making mechanisms. Overall, these findings indicate the translational potential of clinically-relevant computational parameters for precision psychiatry.

Testing Prospect Theory Parameters and the Impact of Human Capital in the Business Domain

Testing Prospect Theory Parameters and the Impact of Human Capital in the Business Domain

A simple non-parametric method for eliciting prospect theory's value function and measuring loss aversion under risk and ambiguity

Prospect theory emerged as one of the leading descriptive decision theories that can rationalize a large body of behavioral regularities. The methods for eliciting prospect theory parameters, such as its value function and probability weighting, are invaluable tools in decision analysis. This paper presents a new simple method for eliciting prospect theory’s value function without any auxiliary/simplifying parametric assumptions. The method is applicable both to choice under ambiguity (Knightian uncertainty) and risk (when events are characterized by objective probabilities). Our new elicitation method is implemented in a simple paper-and-pencil experiment (via an iterative multiple price list format). This is one of the first experiments that elicits non-parametric prospect theory’s value function with salient rewards. The collected data generally confirm findings in the existing literature: the value function is S-shaped (concave in the gain domain and convex in the loss domain) though there is a weaker loss aversion on the aggregate level and a substantial heterogeneity in loss aversion on the individual level (41% loss averse, 6% loss neutral and 53% gain seeking).

Capitalizing on prospect theory value: The Asian developed stock markets

This study shows that a stock whose past return distribution has a high (low) prospect theory value earns a low (high) subsequent return in the stock markets in Hong Kong and Singapore as well as in Japan. In addition, it investigates whether appropriate components of the value function and the probability weighting function that capitalize on prospect theory value are different across countries due to the different risk attitudes of investors. The parameter estimates show that each stock market has different cumulative prospect theory parameters for better performance, and the level of loss aversion for each market is lower than the original values offered by Tversky and Kahneman (1992).

Prospect Theoretic Analysis of Privacy-Preserving Mechanism

We study a problem of privacy-preserving mechanism design. A data collector wants to obtain data from individuals to perform some computations. To relieve the privacy threat to the contributors, the data collector adopts a privacy-preserving mechanism by adding random noise to the computation result, at the cost of reduced accuracy. Individuals decide whether to contribute data when faced with the privacy issue. Due to the intrinsic uncertainty in privacy protection, we model individuals' privacy-related decision using Prospect Theory. Such a theory more accurately models individuals' behavior under uncertainty than the traditional expected utility theory, whose prediction always deviates from practical human behavior. We show that the data collector's utility maximization problem involves a polynomial of high and fractional order, the root of which is difficult to compute analytically. We get around this issue by considering a large population approximation, and obtain a closed-form solution that well approximates the precise solution. We discover that the data collector who considers the more realistic Prospect Theory based individual decision modeling would adopt a more conservative privacy-preserving mechanism, compared with the case based on the expected utility theory modeling. We also study the impact of Prospect Theory parameters, and concludes that more loss-averse or risk-seeking individuals will trigger a more conservative mechanism. When individuals have different Prospect Theory parameters, simulations demonstrate that the privacy protection first becomes stronger and then becomes weaker as the heterogeneity increases from a low value to a high one.

Prospect theory and energy efficiency

Investments in energy efficiency entail uncertainty, and when faced with uncertainty consumers have been shown to behave according to prospect theory: preferences are reference-dependent and exhibit loss aversion, and probabilities are subjectively weighted. Using data from a choice experiment eliciting prospect theory parameters, I provide evidence that loss-averse people are less likely to invest in energy efficiency. Then, I consider policy design under prospect theory when there are also externalities from energy use. A higher degree of loss aversion implies a higher subsidy to energy efficiency. Numerical simulations suggest that the impact of prospect theory on policy may be substantial.

Influence modeling: Mathematical programming representations of persuasion under either risk or uncertainty

Abstract Persuasion is a fundamental element of human interaction applied to both individuals and populations. Although persuasion is a well-studied, interdisciplinary field of research, this work advances its prescriptive, quantitative characterization, and future use. That is, this research complements the qualitative psychological literature with respect to the processing of persuasive messages by developing mathematical programming formulations to identify an optimal influence campaign. We adapt the classic Decision Analysis problem to a bilevel mathematical program, wherein a persuader has the opportunity to affect the environment prior to the decisionmaker’s choice. Thereby, we define a new class of problems for modeling persuasion. Utilizing Cumulative Prospect Theory as a descriptive framework of choice, we transform the persuasion problem to a single level mathematical programming formulation, adaptable to conditions of either risk or uncertainty. These generalized models allow for the malleability of prospects as well as Cumulative Prospect Theory parameters through persuasion update functions. We detail the literature that supports the quantification of such effects which, in turn, establishes that such update functions can be realized. Finally, the efficacy of the model is illustrated through three use cases under varying conditions of risk or uncertainty: the establishment of insurance policies, the construction of a legal defense, and the development of a public pension program.

Identification of cumulative prospect theory parameters for mode choice model

The use of Cumulative Prospect Theory (CPT) in decision making related to transportation risk is still much debated. Mainly because of the travel and socio-economic characteristics of the traveller it possible for different responses to the specified Reference Point (RP) as well as the loss aversion. This difference can be seen from the value of Cumulative Prospect Theory parameters. Therefore, this paper will discuss about the determination of parameters CPT which affect public transportation mode choice model in the course of work trip activity. The reference point as an essential part of this study is determined based on the average travel time of commuter worker from South Tangerang City to Jakarta. Data obtained from stated preference survey, Feeder Busway/Busway and Commuter Line Jabodetabek as mode alternative and travel time attribute as a risk factor. The Binomial Logit model which has transformed utility distribution and probability with CPT and the Least Square Method to be obtained the parameters. Finally, some conclusions can be drawn that the CPT parameters produced by this study, have closed the range of value requirements in the CPT theory. So that the parameter value can be used to model the probability of mode choice with the risk of travel time in the study area.

Heterogeneity in loss aversion: evidence from field elicitations

PurposeProspect theory is now widely accepted as the dominant model of choice under risk, but has not been fully incorporated into applied research because of uncertainty about how to include population-level parameter estimates. The purpose of this paper is to characterize heterogeneity across people to lay a foundation for future applied research.Design/methodology/approachThe paper uses elicitation data from field experiments in Vietnam to fit a finite Gaussian mixture model using the expectation maximization algorithm. Applied results are simulated for investment allocations under myopic loss aversion.FindingsThe authors find that about 20 percent of the sample is classified as extremely loss averse, while the rest of the population is only mildly loss averse. This implies a bimodal distribution of loss aversion in the population.Research limitations/implicationsThe data set is only moderately sized: 181 subjects. Future research will be needed to extend these results out of sample, and to other regions.Originality/valueThis paper provides empirical evidence that heterogeneity matters in prospect theory modeling. It highlights how policy makers might be misled by assuming that average prospect theory parameters are typical within the population.

Estimating cumulative prospect theory parameters from an international survey

We conduct a standardized survey on risk preferences in 53 countries worldwide and estimate cumulative prospect theory parameters from the data. The parameter estimates show that significant differences on the cross-country level are to some extent robust and related to economic and cultural differences. In particular, a closer look on probability weighting underlines gender differences, economic effects, and cultural impact on probability weighting. The data set is a useful starting point for future research that investigates the impact of risk preferences on the market level.

Taming Models of Prospect Theory in the Wild? Estimation of Vlcek and Hens (2011)

Shortcomings revealed by experimental and theoretical researchers such as Allais (1953), Rabin (2000) and Rabin and Thaler (2001) that put the classical expected utility paradigm von Neumann and Morgenstern (1947) into question, led to the proposition of alternative and generalized utility functions, that intend to improve descriptive accuracy. The perhaps best known among those alternative preference theories, that has attracted much popularity among economists, is the so called Prospect Theory by Kahneman and Tversky (1979) and Tversky and Kahneman (1992). Its distinctive features, governed by its set of risk parameters such as risk sensitivity, loss aversion and decision weights, stimulated a series of economic and financial models that build on the previously estimated parameter values by Tversky and Kahneman (1992) to analyze and explain various empirical phenomena for which expected utility doesn't seem to offer a satisfying rationale. In this paper, after providing a brief overview of the relevant literature, we take a closer look at one of those papers, the trading model of Vlcek and Hens (2011) and analyze its implications on Prospect Theory parameters using an adopted maximum likelihood approach for a dataset of 656 individual investors from a large German discount brokerage firm. We find evidence that investors in our dataset are moderately averse to large losses and display high risk sensitivity, supporting the main assumptions of Prospect Theory.

External validity of prospect theory: The evidence from soccer betting

This paper tests whether the prospect theory parameters estimated from laboratory experiments correspond to estimates from real-life betting markets. Using Czech soccer betting data, we estimate the functional forms of the value and probability weighting functions commonly used for the experimental validation of prospect theory. In line with the experimental evidence, we find that bettors are risk averse in the domain of gains and risk seeking in the domain of losses and tend to overweight small probabilities and underweight medium and large probabilities. On the other hand, our findings suggest that bettors do not exhibit loss aversion. This might be at least partly explained by recent experimental evidence suggesting that loss aversion is weaker or absent if the decision-makers are experienced, if they face similar choices repeatedly, and if the decisions are made in a context where offers are usually accepted.

Time-based versus money-based decision making under risk: An experimental investigation

This paper investigates whether individuals make similar decisions under risk when the outcomes are expressed in time versus monetary units. We address this issue in two studies measuring individual risk preferences and prospect theory parameters (i.e., utility curvature, probability weighting, and loss aversion) for both time and money. In the first (resp., second) study we consider relatively small (resp., large) time and monetary outcomes. We find that individuals hold similar risk preferences for time and money; we also find evidence that “time is money” with regard to the utility curvature for gains, loss aversion, and decision weighting. However, individuals have different valuations of losing time and money. The utility function for small losses of money is more concave and variable than the utility function for small losses of time (Study 1), but the utility function for large losses of time is more concave and variable than that for large losses of money (Study 2). We argue that these results reflect a difference in the perceived slack of the respective resource.

Belief in Mean Reversion and the Disposition Effect: An Experimental Test

The disposition effect refers to the investors’ tendency to disproportionately sell more winning than losing assets. This experiment evaluates its two competing behavioral mechanisms: belief in mean reversion and prospect theory. The participants were endowed with some hypothetical assets, observed their price sequences and made selling decisions. Sixty-one percent of them exhibited significant disposition effect. I elicited the participants’ prospect theory parameters and beliefs about price movements, and found that beliefs especially in the loss domain, not prospect theory, significantly contribute to the between-subject variation in the disposition effect. The results from a goodness-of-fit test also favor the belief mechanism.

Prospect Theory for joint time and money consequences in risk and ambiguity

Transport users face complex decisions. Not only are the consequences of their choices uncertain, but they generally involve several attributes, such as time and money. Time-money tradeoffs have been studied in depth in transport economics, and research is now paying increasing attention to the role of uncertainty and information in transport decisions. This paper aims to measure the impact of uncertainty and information on multi-attribute decisions using Prospect Theory. In doing so, the study makes two contributions to transportation literature: one methodological and the other empirical. First, we propose a fast and tractable method for measuring Prospect Theory parameters that capture attitudes towards probabilities (probability weighting function) and attitudes towards losses (loss aversion). The elicitation method does not require the elicitation of the utility function. This makes it particularly suitable in complex multi-attribute decisions where the shape of the utility function is unknown. Second, we present the results of an experiment that uses the proposed method to measure, at the individual level, probability weighting in decisions involving joint time and money consequences in two decision contexts: risk (where probabilities are given) and ambiguity (where the probability distribution is unknown). An experimental setup that exposes subjects to real gains and losses for money and time has been built for this purpose. We observe inverse S-shaped probability weighting and loss aversion for risk. Probability weighting is even more pronounced in ambiguity, where subjects do not have precise information about the probability distribution. We explain how these results and the analysis of ambiguity attitudes in general can offer a better understanding of travelers’ route or transport mode choices.

What Are Investors Willing to Pay to Customize Their Investment Product?

Even though buy-and-hold (B&amp;H) investment strategies can take the risk tolerance of an investor into account by specifying a suitable stock proportion, the outcome profiles of B&amp;H strategies are restricted to a specific class of return distributions. For investors with particular risk preferences, further customization should thus provide additional value. The objective of this paper is to investigate the strength of preference for such customized distributions and to draw conclusions about the demand for personalized investment products. In two experimental studies, 256 participants could adjust the return distribution of an initially chosen B&amp;H investment by using an interactive software program. Our main finding is that most investors make extensive use of the customization option and many are willing to pay a substantial fee for this additional flexibility. We further find that the willingness to pay for customization is lower if the fee is integrated into the display of the return distribution, making its impact on final returns more obvious. We also observe that investors can be clustered into distinct subgroups via their adjustment patterns, but individually elicited prospect theory parameters are barely able to explain and predict these adjustments. As a robustness check, we also survey real investors at an investors fair to compare their preferences with those of our main pool of student subjects. We find that the willingness to pay for customization is slightly lower for these real investors and the main effect of fee integration is also less pronounced. In summary, we observe a strong willingness to pay for additional flexibility even though the actual benefits of customization vary markedly according to the individual. In many cases the accepted fees are so high that standard B&amp;H strategies stochastically dominate the customized distributions after fee integration. This paper was accepted by Peter Wakker, decision analysis.

Genetic Algorithm to Estimate Cumulative Prospect Theory Parameters for Selection of High-Occupancy-Vehicle Lane

Recent literature suggests a need for a more realistic representation of driver behavior. In an effort to integrate prospect theory as a potential descriptive method into traveler behavior, it is important to determine the validity of previous estimated parameters obtained from empirical studies and interviews of people who are not in the same fast-paced, dynamic, travel time disutility setting as real drivers. A genetic algorithm is used to simultaneously estimate the parameters of the cumulated prospect theory (CPT) value and weight functions as well as the coefficients of the random utility model; this procedure leads to estimates that have a higher likelihood value and statistical significance than an equivalent expected utility–based logit model or a CPT-based logit model using the empirical values developed earlier. The value function parameters generally conform to conclusions from previous literature. The weight function parameters, however, suggest that drivers in a fast-paced changing environment with multiple subjects for prospect evaluation may become overwhelmed by the certainty effect.

What are Investors Willing to Pay to Customize Their Investment Product?

Even though buy-and-hold (B&H) investment strategies can take into account the investor’s risk tolerance by fixing a suitable stock proportion, the outcome profiles of B&H strategies are restricted to a certain class of distributions. For investors with specific risk preferences, further customization should thus provide additional value. The paper’s objective is to investigate the strength of preference for such customized distributions and to draw conclusions about the demand for personalized investment products. In an experimental study, 149 participants could adjust the return distribution of an initially chosen B&H investment by use of an interactive software program. As our main finding, we observe that (1) most investors have a strong preference for customization and many are willing to pay so much for such customization that dominance violations result. As further interesting contributions to the literature, we observe that (2), on average, investors do not act skewness seeking during customization, (3) can be clustered into distinct subgroups via their adjustment patterns and (4) do not adjust the B&H distributions in accordance with individually elicited prospect theory parameters. In summary, we observe a strong willingness to pay for additional flexibility even though the actual benefits of customization vary largely by the individual.