Rank-dependent Expected Utility Research Articles

A game model and numerical simulation of risk communication in metro emergencies under the influence of emotions

To study the influence of subject emotions on risk communication under emergencies, this paper adopts the Rank Dependent Expected Utility (RDEU) theory to define sentiment functions. Using a metro emergency as an example, a game model of risk communication between the public and the management is constructed, then a Nash equilibrium solution analysis is conducted, and finally a numerical simulation using MATLAB is carried out to investigate the optimal strategy for risk communication in different situations. The results show that emotions can affect the risk communication behaviour of the emergency to a certain extent, but are not a determining factor. When both sides of the game have emotions, the pessimistic emotional state will have a greater impact on decision-making compared to the optimistic emotional state. In addition, it is found that opinion leaders significantly influence the choice of risk communication strategies of game players. This study provides theoretical and methodological support for risk communication in emergencies.

How emotion type and intensity affect rumor spreading

The implications and contagion effect of emotion cannot be ignored in rumor spreading. This paper sheds light on how decision makers’ (DMs) emotion type and intensity affect rumor spreading. Based on the rank-dependent expected utility (RDEU) and evolutionary game theory (EGT), we construct an evolutionary game model between rumormongers (RMs) and managers (Ms) by considering emotions. We use MATLAB to simulate and reveal the influencing mechanism of DMs’ emotion type and intensity on rumor spreading. The results indicate that the DMs’ strategy choice is not only affected by their own emotion preference and intensity, but also by the other players in rumor spreading. Moreover, pessimism has a more significant influence than optimism on the stability of the evolutionary game, Ms’ emotion is more sensitive to the game results than RMs’ emotion and the emotion intensity is proportional to the evolution speed. More significantly, some earthshaking emotional thresholds are found, which can be used to predict RMs’ behavior, help Ms gain critical time to deal with rumors, and avoid the Tacitus Trap crisis. Furthermore, the evolution results fall into five categories: risk, opportunity, ideal, security and hostility. The results of this work can benefit Ms’ public governance.

How Does Public Sentiment Affect the Socially Responsible Behavior of Construction Enterprises?

The negative environmental impact of the construction sector has garnered global attention, and as the “primary force” in achieving the “double carbon” target, green development is urgent, and social responsibility practices cannot be postponed. An evolutionary game model was constructed by combining the rank-dependent expected utility (RDEU) theory and the evolutionary game theory to understand the interaction mechanism between participants’ emotions and decisions, taking into account the characteristics of construction enterprises and the public regarding irrational decisions under heterogeneous emotional combinations. The study demonstrates that: (1) there is probability in the choice of rational strategies, and emotion is an irrational factor that can affect strategy choice. (2) The evolutionary trend of the strategy choice of the game subjects is altered by emotional intensity and emotional propensity. The optimism of construction enterprises inhibits their socially responsible practice, and the pessimism of the public promotes the probability of their negative strategy choice. Furthermore, moderate optimism is a safety valve for the public’s positive strategy choice. (3) The interaction of emotional states leads to a heterogeneity of strategy choices exhibited under different combinations of emotions, with the emotions of construction companies having a more dominant influence on strategy. Finally, we make some feasible recommendations for improving social responsibility practices and preventing mass incidents by boosting emotional monitoring and guidance for construction businesses and the general public. Overall, this study provides important information about how to be socially responsible, maintain good relationships with the public, and protect the environment.

Evolutionary Game Analysis of Shared Manufacturing Quality Innovation Synergetic Behavior Considering a Subject’s Heterogeneous Emotions

Shared manufacturing provides a new path for the transformation and development of the manufacturing industry, but challenges such as low quality and poor positivity for quality improvement limit the positive role of shared manufacturing. Considering the influences of heterogeneous emotions of subjects on quality decision making, the theory of rank-dependent expected utility (RDEU) and evolutionary game theory were integrated to establish an evolutionary game model of shared manufacturing quality innovation synergy with multi-agent participation and analyze how sentiment affects motivation for quality improvement. The study showed that: (1) emotions, an irrational factor, can significantly change the stable state of the evolution of the shared manufacturing quality innovation synergetic system by influencing the decision-making behavior of decision makers; (2) in terms of the specific microscopic influence mechanism, rationality is the key to ensuring that the behavioral decisions of decision makers do not enshrine large systemic deviations. (3) In terms of the mechanism of heterogeneous emotions, when one party is optimistic, the deepening of the other party’s pessimism tends to bring positive effects; when one party is pessimistic, the deepening of the other party’s optimism tends to bring negative effects. The main management insights are as follows: (1) correctly recognizing and treating heterogeneous emotions of decision makers and regulating the formation and role of heterogeneous emotions of decision makers; (2) appropriately creating an atmosphere of pessimistic emotions, and guiding shared manufacturing to pay attention to manufacturing quality innovation synergy; (3) appropriately releasing favorable information about quality innovation synergy, and continuously promoting high-quality development of shared manufacturing. This study broadens the path of quality improvement in shared manufacturing and the scope of application of emotion theory in a certain sense.

RDEU hawk-dove game analysis of the China-Australia iron ore trade conflict

By combining rank dependent expected utility (RDEU) theory model with asymmetric hawk-dove game model, this paper builds the RDEU hawk-dove game model to resolve the iron ore trade conflict between Chinese steel companies and Australian iron ore companies. Moreover, the impact of corporate benefits, conflict costs, “emotional factors” and “asymmetric factors” on corporate strategic choices are considered comprehensively. The study finds that:(1) When the benefits of Chinese and Australian companies are less than the conflict costs, there are the following conclusions. First, concerning the “emotional factors”, compared with optimism, pessimism has greater impact on the strategic choices of Chinese and Australian companies. Second, the greater the degree of asymmetry in the pricing power of Chinese and Australian companies, more Australian iron ore companies tend to choose the extreme confrontation strategy, and more Chinese steel companies tend to choose the peaceful settlement strategy. Finally, when the emotional factors and asymmetric factors are equal, compared with Chinese companies, the probability of Australian companies adopting the extreme confrontation strategy is higher, which is mainly due to the higher incomes of Australian companies. (2) When the benefits of Chinese companies are less than the conflict costs and the benefits of Australian companies are greater than the conflict costs, regardless of the emotions of both parties in the game, Australian companies tend to choose the extreme confrontation strategy, and Chinese companies tend to choose the peaceful settlement strategy. (3) When the benefits of Chinese and Australian companies are greater than the conflict costs, regardless of the emotions of both parties in the game, Chinese and Australian companies tend to choose extreme confrontation strategy. The research results can provide a reference for Chinese and Australian companies to resolve iron ore trade conflicts.

Robust Risk-Aware Reinforcement Learning

We present a reinforcement learning (RL) approach for robust optimization of risk-aware performance criteria. To allow agents to express a wide variety of risk-reward profiles, we assess the value of a policy using rank dependent expected utility (RDEU). RDEU allows agents to seek gains, while simultaneously protecting themselves against downside risk. To robustify optimal policies against model uncertainty, we assess a policy not by its distribution but rather by the worst possible distribution that lies within a Wasserstein ball around it. Thus, our problem formulation may be viewed as an actor/agent choosing a policy (the outer problem) and the adversary then acting to worsen the performance of that strategy (the inner problem). We develop explicit policy gradient formulae for the inner and outer problems and show their efficacy on three prototypical financial problems: robust portfolio allocation, benchmark optimization, and statistical arbitrage.

Optimal insurance to maximize RDEU under a distortion-deviation premium principle

In this paper, we study an optimal insurance problem for a risk-averse individual who seeks to maximize the rank-dependent expected utility (RDEU) of her terminal wealth, and insurance is priced via a general distortion-deviation premium principle. We prove necessary and sufficient conditions satisfied by the optimal solution and consider three orders between the distortion functions for the buyer and the seller to further determine the optimal indemnity. Finally, we analyze examples under three distortion-deviation premium principles to explore the specific conditions under which no insurance or deductible insurance is optimal.

Sequential Decision Making with Rank Dependent Utility: A Minimax Regret Approach

This paper is devoted to sequential decision making with Rank Dependent expected Utility (RDU). This decision criterion generalizes Expected Utility and enables to model a wider range of observed (rational) behaviors. In such a sequential decision setting, two conflicting objectives can be identified in the assessment of a strategy: maximizing the performance viewed from the initial state (optimality), and minimizing the incentive to deviate during implementation (deviation-proofness). In this paper, we propose a minimax regret approach taking these two aspects into account, and we provide a search procedure to determine an optimal strategy for this model. Numerical results are presented to show the interest of the proposed approach in terms of optimality, deviation-proofness and computability.

Game analysis of nuclear wastewater discharge under different attitudes: Seeking a potential equilibrium solution

Marine pollution is an increasingly dangerous problem, affecting people across the world. Japan's decision on 13 April 2021 to discharge nuclear wastewater into the sea has aroused the close attention of interest-related countries. To resolve conflicts among various countries and achieve the harmonious development of the marine and economic environment, we employ the static game, the rank-dependent expected utility (RDEU) game, and the sequential game to comprehensively analyze the equilibrium strategies of discharge country and interest-related countries under different situations. Our analysis reveals that in the static game and sequential game where interest-related countries make decisions first, the discharge behavior of the discharge country should be restricted from the perspective of the internal and external benefits of the discharge country. In addition, when integrating changes in emotion into the game, it can be found that the most expected emotional state to prevent the discharge country from discharging nuclear wastewater for interest-related countries is to remain pessimistic. Overall, this study provides important implications for inter-state relations and environmental protection.

Rank-dependent preferences, social network and crop insurance uptake: field experimental evidence from rural China

PurposeAgricultural insurance has become increasingly important to farmers' livelihood and production in rural China. Yet despite the enormous governmental subsidizing efforts, the insurance participation rate remains below expectations. This study revisits the linkage between farmers' risk attitudes and crop insurance utilization by providing a cross-cutting perspective such that the role of risk aversion is re-scrutinized in Chinese “kindred” village economies.Design/methodology/approachThe authors administrated a lottery-based multiple price list (MPL) experiment by recruiting rice farmers from 12 villages in Sichuan province in southwestern China. Using the experimental data, farmers' risk attitudes are assessed and coefficients of risk aversion are estimated within the rank-dependent expected utility (RDEU) framework by maximizing a structured likelihood function.FindingsThis study provides substantiating evidence that rice farmers in southwestern China exhibit relatively high risk aversion. The authors also provide suggestive evidence of the positive relationship between farmers' risk aversion and crop insurance utilization. In addition, findings reveal that kinship network has a negative effect on crop insurance utilization, such that farmers who are connected in higher degree of kinship network have lower likelihood of crop insurance utilization, which suggests that kinship network may be substitute for formal crop insurance. Result also demonstrates that the incentive effect of risk aversion on farmers' crop insurance participation manifests differently depending on the degree of kinship network in rural China.Originality/valueThis study provides a cross-cutting perspective by scrutinizing the effects of farmers' risk attitudes and kinship network on crop insurance participation in rural China, which has received relatively little attention in the literature. Conclusions on the effects of risk aversion on crop insurance participation have been mixed in previous studies. In addition, to the best of our knowledge, little has been done to explicitly examine the influence of social proximity and networks on farmers' insurance uptake. This study attempts to fill both gaps. This study provides new insights which might shed lights on the understanding of farmers' crop insurance participation in rural China.

Robust Risk-Aware Reinforcement Learning

We present a reinforcement learning (RL) approach for robust optimisation of risk-aware performance criteria. To allow agents to express a wide variety of risk-reward profiles, we assess the value of a policy using rank dependent expected utility (RDEU). RDEU allows the agent to seek gains, while simultaneously protecting themselves against downside events. To robustify optimal policies against model uncertainty, we assess a policy not by its distribution, but rather, by the worst possible distribution that lies within a Wasserstein ball around it. Thus, our problem formulation may be viewed as an actor choosing a policy (the outer problem), and the adversary then acting to worsen the performance of that strategy (the inner problem). We develop explicit policy gradient formulae for the inner and outer problems, and show its efficacy on three prototypical financial problems: robust portfolio allocation, optimising a benchmark, and statistical arbitrage

Pareto-optimal reinsurance policies with maximal synergy

Optimal reinsurance policies have been studied extensively in the economics and insurance literature. Two types of optimality criteria, expected utility (EU) maximization and risk minimization, are commonly used. Understandably, applying the two types of criteria usually will result in different “optimal” policies. To reconcile the conflicting interests of the insurer and reinsurer and strike a balance between EU maximization and risk minimization, we follow the approach in Borch (1960b) but assume that the involved two parties both apply distortion risk measures instead of variance. We first identify a set of reinsurance policies that minimize the total risk borne by the two parties, then we take this set of policies as admissible and derive the Pareto-optimal policies that maximize the weighted EU of these two parties. A Nash bargaining model is applied to identify the “best” weights allocated to the two parties. In addition, we extend our results to a situation where the insurer’s decision making is dictated by the rank-dependent expected utility (RDEU) theory. Finally, we present numerical examples to show the applicability of our methodology and some implications of the obtained results.

Investigation of the Stochastic Choice under Risk using Experimental Data

This paper extends the analysis of the data from the experiment undertaken by Pradiptyo et al. (2015), to help explain the subjects’ behaviour when making decisions under risk. This study specifically investigates the relative empirical performance of the two general models of the stochastic choice: the random utility model (RUM) and the random preference model (RPM) where this paper specifies these models using two preference functionals, expected utility (EU) and rank-dependent expected utility (RDEU). The parameters are estimated in each model using a maximum likelihood technique and run a horse-race using the goodness-of-fit between the models. The results show that the RUM better explains the subjects’ behaviour in the experiment. Additionally, the RDEU fits better than the EU for modelling the stochastic choice. 

Optimism and pessimism in bargaining and contests

This paper uses the rank-dependent expected utility (RDEU) model to capture the effects of optimism and pessimism on the choice between a pre-trial settlement and a trial (or more generally, between a private settlement and a litigation). These two legal procedures are described as a bargaining game and a contest game, respectively. My models predict that a contest occurs if the aggregate optimism premium in a contest (AOPC) is sufficiently high. I also find that the AOPC tends to be higher for close cases. Such predictions are consistent with the Priest-Klein empirical observation that a plaintiff's winning probability is often near 50% in many areas of civil litigation. I also show that the highest levels of effort in both a bargaining game and a contest game are exerted when one is moderately optimistic. However, excessive optimism will reduce one's effort level, and hence, one's winning rate. As a result, when faced with an excessively optimistic party, a risk-neutral party may prefer a contest over bargaining.

The new models of decision in risk: A critical review of the literature

Abstract. The aim of the risk decision theory is to describe the behavior of agents in the face of several random prospects. Since it is difficult to describe these preferences, we seek to represent them. The use of a representative function of preferences has been for a long time, the usual method of describing behavior in a random context. The obvious advantage of this method is that it allows including these data in a formalized model and, by extension, to understand the optimization process underlying any decision. The determination of the representative function of preferences must be based on an axiomatic basis. From these axioms, an accurate specification of the value function will be derived. The purpose of this article is to examine the history of theories that have sought to determine a satisfactory criterion for responding to the risk decision problem and to analyze the contribution of these models. Keywords. Risk aversion, Expected Utility (EU), Rank Dependent Expected Utility (RDEU), Gamble. JEL. D81, C91.

Investigation of the Stochastic Choice under Risk using Experimental Data

We extend the analysis of the data from the experiment of Pradiptyo et al.’s (2015) to help explaining the subjects’ behaviour on decision under risk. We investigate the relative empirical performance of the two general models of the stochastic choice: the random utility model (RUM) and the random preference model (RPM). We specify these models using two preference functionals, expected utility (EU) and rank-dependent expected utility (RDEU). We then estimate parameters in each model using a maximum likelihood technique and run a horse-race using the goodness-of-fit between the models. The results show that the RUM better explains the subjects’ behaviour in the experiment. Additionally, the RDEU fits better than that of the EU in modelling the stochastic choice.

Optimal insurance under rank-dependent expected utility

We re-visit the problem of optimal insurance design under Rank-Dependent Expected Utility (RDEU) examined by Bernard et al. (2015), Xu (2018), and Xu et al. (2018). Unlike the latter, we do not impose the no-sabotage condition on admissible indemnities, that is, that indemnity and retention functions be nondecreasing functions of the loss. Rather, in a departure from the aforementioned work, we impose a state-verification cost that the insurer can incur in order to verify the loss severity, hence automatically ruling out any ex post moral hazard that could otherwise arise from possible misreporting of the loss by the insured. We fully characterize the optimal indemnity schedule and discuss how our results relate to those of Bernard et al. (2015) and Xu et al. (2018). We then extend the setting by allowing for a distortion premium principle, with a distortion function that differs from that of the insured, and we provide a characterization of the optimal retention in that case.

Optimal Insurance Under Rank-Dependent Expected Utility

We re-visit the problem of optimal insurance design under Rank-Dependent Expected Utility (RDEU) examined by Bernard et al. (2015), Xu (2018), and Xu et al. (2015). Unlike the latter, we do not impose the no sabotage condition on admissible indemnities, that is, the comonotonicity of indemnity functions and retention functions with the loss. Rather, in a departure from the aforementioned work, we impose a state-verification cost that the insurer can incur in order to verify the loss severity, hence automatically ruling out any ex post moral hazard that could otherwise arise from possible misreporting of the loss by the insured. Hence, monotonicity properties of indemnification schedules become of second-order concern. We fully characterize the optimal indemnity schedule and discuss how our results relate to those of Bernard et al. (2015) and Xu et al. (2015). We then extend the setting by allowing for a distortion premium principle, with a distortion function that differs from that of the insured, and we provide a characterization of the optimal retention in that case.

Extreme-aggregation measures in the RDEU model

In order to characterize the most superadditive behavior of a risk measure, the notion of extreme-aggregation risk measures was introduced in the literature. In this short note, explicit forms of the extreme-aggregation measures induced by rank-dependent expected utility (RDEU) functionals and by RDEU-based shortfall risk measures are derived. The main results generalize those known in the literature.

The average risk sharing problem under risk measure and expected utility theory

In this paper, we investigate an average risk sharing problem, in which the optimal objective function is called an average-inf-convolution. We study the properties of the average-inf-convolution for a general risk measure, and obtain the explicit form of the average-inf-convolution. We also analyze the average risk sharing problems in the classic utility models in behavioral economics. Explicit forms of the average-inf-convolutions are obtained in the expected utility model and in the utility-based shortfall model, respectively. In the rank-dependent expected utility (RDEU) model, we give a lower bound of the average-inf-convolution for the RDEU-based shortfall.