Minimizing Regret: The General Case

In repeated games with differential information on one side, the labelling “general case” refers to games in which the action of the informed player is not known to the uninformed, who can only observe a signal which is the random outcome of his and his opponent's action. Here we consider the problem of minimizing regret (in the sense first formulated by J. Hannan (1956, in Contributions to the Theory of Games, Vol. III, Annals of Mathematics Studies, Vol. 39, Princeton, NJ: Princeton Univ. Press.) when the information available is of this type. We give a simple condition describing the approachable set. Journal of Economic Literature Classification Number: D81, D82, D83.     

On the natural selection rule in general linear models

We consider a problem of selecting the best treatment in a general linear model. We look at the properties of the natural selection rule. It is shown that the natural selection rule is minimax under to “0–1” loss function and it is a Bayes rule under a monotone permutation invariant loss function with respect to a permutation invariant prior for every variance balanced design. Some other condition on the design matrix is given so that a Bayes rule with respect to a normal prior will be of simple structure.     

‘Fear of Missing Out’ (FOMO) marketing appeals: A conceptual model

The ‘Fear of Missing Out’ (‘FOMO’) is a well-known concept in popular culture. Consequently, it has been co-opted and successfully utilised in commercial advertising appeals to initiate sales. However, academic research to date has focussed exclusively on FOMO as an individual trait leading to self-initiated FOMO-driven behaviours. By contrast, the success of FOMO sales appeals relies upon consumers’ responses; therefore, it is necessary to understand these response mechanisms. This is the first known academic research to investigate consumer response mechanisms in relation to externally initiated FOMO appeals. In doing so, this research develops an original taxonomy of FOMO appeals; establishes a thematic map of response elements; identifies theory relevant to individuals’ responses; formulates an operational response model; and proposes a future FOMO research agenda.     

The Impact of Regret on Exports

We examine optimal production and export decisions of a firm facing exchange rate uncertainty, where the firm's management is not only risk averse but also regret averse, i.e., is characterized by a utility function that includes disutility from having chosen ex post suboptimal alternatives. Experimental and empirical results support the view that managers tend to be regret averse. Under regret aversion a negative risk premium need not preclude the firm from exporting which would be the case if the firm were only risk averse. Exporting creates an implicit hedge against the possibility of regret when the realized spot exchange rate turns out to be high. The regret‐averse firm as such has a greater ex ante incentive to export than the purely risk averse firm. Finally, we use a two‐state example to illustrate that the firm optimally exports more (less) to the foreign country than in the case of pure risk aversion if the low (high) spot exchange rate is more likely to prevail. Regret aversion as such plays a crucial role in determining the firm's optimal allocation between domestic sales and foreign exports.     

Consumer power and choice deferral: The role of anticipated regret

This paper examines the influence of social power on consumers' propensity to defer choice. Based on the notion that elevated power reduces regret anticipation—the fear of making a wrong choice—it is proposed that power influences the extent of choice deferral by reducing consumers' susceptibility to anticipated regret. Because of the regret-based mechanism, power can increase or decrease consumers' propensity to defer choice, depending upon the situational factors that are associated with anticipated regret, such as salience of regret, outcome reversibility (e.g., return policy), and locus-of-regret (postponing vs. choosing now). Using different manipulations of power, seven studies provide consistent support for the proposed effects and show that situational factors and marketing strategies can induce, turn off, or even reverse the effect of power on deferral. Theoretical contributions and managerial implications are discussed.     

A comparison of regret-based and utility-based discrete choice modelling – an empirical illustration with hospital bed choice

There is some concern that the unobserved preference heterogeneity in random utility maximization theory-based discrete choice experiment modelling is an important source of error variability. The randomness in utility is often interpreted as interpersonal preference heterogeneity but it can also be intrapersonal random variation in preferences. We compare utility maximization and regret minimization-based choice models’ sensitivity to individual heterogeneity, examine differences between two consecrated models and validate with empirical illustrations. We use frequency of category (public, semi-private, and private) of bed chosen from Swiss cross-sectional datasets (2007–2012) to compare two approaches – utility maximization and regret minimization by applying multinomial logit (MNL) models in regard to the variances in utility (regret) function, goodness-of-fit and predicted marginal effects (pseudo-elasticity) of additional payment. We find parameters with the same sign and estimates with almost same order of magnitude in both the approaches. The statistical significance of attribute effects is consistent in all variants of utility -based MNL models while effects of different attributes are significant only in heteroskedastic extreme value (HEV) variant of regret-based MNL models. This empirical illustration suggests that HEV variant of regret-based models perform better in capturing attribute effects in choice behaviour.     

价格变化、后悔与交易价值损失对抱怨的影响

利用情景模拟实验设计方法获取数据,并采用结构方程模型研究了价格变化对已购买产品的顾客带来的心理感受和影响,结果发现:当产品实际价格下降水平超过已购买者心理预期时,顾客会感受到交易价值损失,且交易损失感受对顾客的后悔感有显著的正向影响,但交易价值损失并不直接影响顾客抱怨,后悔感受构成了交易损失和顾客抱怨关系的中介变量。     

基于Minimax的漳河流域水资源公平配置

漳河流域水资源冲突激烈的现状,使得公平原则在水资源配置过程中尤其重要。借鉴极小极大值方法,构建漳河流域水资源公平配置模型,并给出模型的求解算法,最后以漳河流域水资源初始配置为例,利用Matlab优化工具箱编程计算得出典型枯水年来水和现状年需水、规划年需水情景下的配置方案。结果表明:模型较好地实现了用户公平性,有效避免了"大锅水"现象。     

Minimax regret treatment choice with covariates or with limited validity of experiments

This paper continues the investigation of minimax regret treatment choice initiated by Manski (2004). Consider a decision maker who must assign treatment to future subjects after observing outcomes experienced in a sample. A certain scoring rule is known to achieve minimax regret in simple versions of this decision problem. I investigate its sensitivity to perturbations of the decision environment in realistic directions. They are as follows. (i) Treatment outcomes may be influenced by a covariate whose effect on outcome distributions is bounded (in one of numerous probability metrics). This is interesting because introduction of a covariate with unrestricted effects leads to a pathological result. (ii) The experiment may have limited validity because of selective noncompliance or because the sampling universe is a potentially selective subset of the treatment population. Thus, even large samples may generate misleading signals. These problems are formalized via a “bounds” approach that turns the problem into one of partial identification.In both scenarios, small but positive perturbations leave the minimax regret decision rule unchanged. Thus, minimax regret analysis is not knife-edge-dependent on ignoring certain aspects of realistic decision problems. Indeed, it recommends to entirely disregard covariates whose effect is believed to be positive but small, as well as small enough amounts of missing data or selective attrition. All findings are finite sample results derived by game theoretic analysis.     

Minimax estimation under convex loss when the parameter interval is bounded

In the present paper families of truncated distributions with a Lebesgue density forx=(x ₁,...,x _n ) ε ℝ ⁿ are considered, wheref ₀:ℝ → (0, ∞) is a known continuous function andC _n (ϑ) denotes a normalization constant. The unknown truncation parameterϑ which is assumed to belong to a bounded parameter intervalΘ=[0,d] is to be estimated under a convex loss function. It is studied whether a two point prior and a corresponding Bayes estimator form a saddle point when the parameter interval is sufficiently small.