Loss Aversion and Bargaining

We consider bargaining situations where two players evaluate outcomes with reference-dependent utility functions, analyzing the effect of differing levels of loss aversion on bargaining outcomes. We find that as with risk aversion, increasing loss aversion for a player leads to worse outcomes for that player in bargaining situations. An extension of Nash's axioms is used to define a solution for bargaining problems with exogenous reference points. Using this solution concept we endogenize the reference points into the model and find a unique solution giving reference points and outcomes that satisfy two reasonable properties, which we predict would be observed in a steady state. The resulting solution also emerges in two other approaches, a strategic (non-cooperative) approach using Rubinstein's (1982) alternating offers model and a dynamic approach in which we find that even under weak assumptions, outcomes and reference points converge to the steady state solution from any non-equilibrium state.     

On Loss Aversion in Bimatrix Games

In this article three different types of loss aversion equilibria in bimatrix games are studied. Loss aversion equilibria are Nash equilibria of games where players are loss averse and where the reference points—points below which they consider payoffs to be losses—are endogenous to the equilibrium calculation. The first type is the fixed point loss aversion equilibrium, introduced in Shalev (2000; Int. J. Game Theory 29(2):269) under the name of ‘myopic loss aversion equilibrium.’ There, the players’ reference points depend on the beliefs about their opponents’ strategies. The second type, the maximin loss aversion equilibrium, differs from the fixed point loss aversion equilibrium in that the reference points are only based on the carriers of the strategies, not on the exact probabilities. In the third type, the safety level loss aversion equilibrium, the reference points depend on the values of the own payoff matrices. Finally, a comparative statics analysis is carried out of all three equilibrium concepts in 2 × 2 bimatrix games. It is established when a player benefits from his opponent falsely believing that he is loss averse.     

The effect of fast and slow decisions on risk taking

We experimentally compare fast and slow decisions in a series of experiments on financial risk taking in three countries involving over 1700 subjects. To manipulate fast and slow decisions, subjects were randomly allocated to responding within 7 seconds (time pressure) or waiting for at least 7 or 20 seconds (time delay) before responding. To control for different effects of time pressure and time delay on measurement noise, we estimate separate parameters for noise and risk preferences within a random utility framework. We find that time pressure increases risk aversion for gains and risk taking for losses compared to time delay, implying that time pressure increases the reflection effect of Prospect Theory. The results for gains are weaker and less robust than the results for losses. We find no significant difference between time pressure and time delay for loss aversion (tested in only one of the experiments). Time delay also leads to less measurement noise than time pressure and unconstrained decisions, and appears to be an effective way of decreasing noise in experiments.     

An axiomatization of cumulative prospect theory

This paper presents a method for axiomatizing a variety of models for decision making under uncertainty, including Expected Utility and Cumulative Prospect Theory. This method identifies, for each model, the situations that permit consistent inferences about the ordering of value differences. Examples of rankdependent and sign-dependent preference patterns are used to motivate the models and the “tradeoff consistency” axioms that characterize them. The major properties of the value function in Cumulative Prospect Theory—diminishing sensitivity and loss aversion—are contrasted with the principle of diminishing marginal utility that is commonly assumed in Expected Utility.     

Reflections on gains and losses: A 2 × 2 × 7 experiment

What determines risk attraction or aversion? We experimentally examine three factors: the gain-loss dichotomy, the probabilities (0.2 vs. 0.8), and the money at risk (7 amounts). We find that the majority display risk attraction for small amounts of money, and risk aversion for larger amounts. Yet the frequency of risk attraction varies according to the gain-loss dichotomy and the probabilities. Kahneman and Tversky studied gain-loss reflections. We submit that a reflection can be decomposed into a translation and a probability switch. We find significant translation and switch effects, which are of comparable magnitude, a result that is equidistant from the diverging two popular views inspired by Prospect Theory: the gain-loss asymmetry, and the fourfold pattern.     

For whom does social comparison induce risk-taking?

A ‘bonus culture’ among financial traders has been blamed for the excessive risk-taking in the run-up to the latest financial crisis. I show that when individuals are more social gain seeking than social loss averse (i.e. gloating is stronger than envy), social comparison predicts more risk-taking as well as a preference for negatively correlated gambles. Testing these two joint propositions in a laboratory experiment, I find that preference for positively or negatively correlated outcomes is highly correlated with risk-taking in a social risky investment task. While only a third of subjects prefer negatively correlated outcomes in a peer comparison setting, in line with relatively stronger social gain seeking, those subjects invest on average 50 % more in a risky gamble in their peer comparison setting than a reference group that made the same decision in an isolated individual setting. Subjects with a preference for positively correlated outcomes, in line with relatively stronger social loss aversion, do not show a higher propensity to invest in a risky gamble compared to the individual reference group.     

Time preferences and risk aversion: Tests on domain differences

Understanding how individuals discount and evaluate the risks of environmental outcomes is a prime component in designing effective environmental policy. We use an incentivized experimental design to investigate whether subjects’ time preferences and risk aversion across the monetary and environmental domains differ. We find that subjects’ time preferences are not significantly different across the two domains. In contrast, subjects exhibit a higher degree of risk aversion in the environmental domain. Furthermore, we corroborate earlier results, documenting that women are more risk averse than men in the monetary domain, and show this finding to also hold in the environmental domain.     

Market failure in light of non-expected utility

This paper merges the non-expected utility approach (Tversky and Kahneman, J Risk Uncertain 5:297–323, 1992 and Quiggin, J Econ Behav Organ 3:323–343, 1982) into Akerlof’s (Quart J Econ 84:488–500, 1970) model of Market for Lemons. We derive the results for different probability weighting functions and analyze the phenomenon of market failure in light of non-expected utility maximization. Our main finding suggests that when the proportion of traded lemons is high (low), the problem of market failure is mitigated (enhanced). In addition, for the case of Cumulative Prospect Theory, we show that (a) the higher the loss aversion is, the more pronounced is the market failure; (b) gain-domain elevation is negatively related to the extent of market failure; and (c) the value function is (i) negatively monotonic in the gain-domain diminishing sensitivity parameter when the market is characterized by a high proportion of “peaches,” and (ii) positively monotonic in the loss-domain diminishing sensitivity parameter when the market is characterized by a high proportion of “lemons.”     

参照群体、相对位置与微观分配公平感:都市户籍移民与流动人口的比较分析

本文详细考察和比较了都市户籍移民和流动人口分配公平感形塑过程中参照群体选择及相对位置效应的内在逻辑，揭示了社会比较机制的具体作用机理。研究发现，在报告分配公平感时，户籍身份成为都市移民选择参照对象的制度性基础，拥有都市户口者方可成为户籍移民的参照对象，而流动人口的参照群体更为开放和多元，倾向于与所有都市常住居民进行比较。与此同时，即便考虑到社会网络结构、迁移时长、迁移世代等因素，结论仍具稳健性，来源地居民均不会被二者视为参照群体。另一方面，实证结果显示，相对位置距离对分配公平感的形塑作用之于户籍移民和流动人口并无显著差异，同时呈现非对称性特征：参照优势地位者体现了“平等主义”心态，参照劣势地位者则表现出“损失厌恶”的特征；相对位置距离的拉大给参照劣势者因损失带来的厌恶情绪大于参照优势者因获益而产生的满足感知。     

Risk taking after absolute and relative wealth changes: The role of reference point adaptation

We conducted an experiment to compare subjects’ attitudes toward risk before and after they experienced wealth changes induced by a real-effort task. We identified and estimated the subjects’ levels of reference point adaptation to absolute and relative wealth changes. We found that after experiencing a larger loss than others, the subjects did not completely adapt their reference points to the absolute wealth loss and the relative negative wealth gap, and thus significantly increased their risk-taking behavior. However, the subjects also did not adjust their attitudes toward risk after experiencing a smaller loss than others, a smaller gain than others, or a larger gain than others. This may be because they promptly adapted to wealth changes or because they did not adapt to wealth changes but the effects of absolute and relative wealth changes mostly offset each other.     

Absolute and relative risk aversion: An experimental study

Kenneth Arrow posed the hypotheses that investors reveal decreasing absolute risk aversion (DARA) and increasing relative risk aversion (IRRA). It is very difficult to empirically test these two hypotheses since one needs to analyze an investor's investment decisions at various points in his/her economic life cycle as the investor's wealth varies. An experimental study is conducted to test these two hypotheses when the subject's wealth varies depending on his/her investment performance. The experiment involves an actual money gain or loss which is indexed to the individual's investment performance. It is found that DARA is indeed strongly supported, but IRRA is rejected.     

Estimating Risk Attitudes using Lotteries: A Large Sample Approach

Attitudes towards risk play a major role in many economic decisions. In empirical studies it is quite often assumed that attitudes towards risk do not vary across individuals. This paper questions this assumption and analyses which factors influence an individual's risk attitude. Based on questions on lotteries in a large household survey we first semiparametrically estimate an index for risk aversion. We only make weak assumptions about the underlying decision process and our estimation method allows for generalisations of expected utility. We then estimate a structural model based on Cumulative Prospect Theory. Expected utility is strongly rejected and both the value function and the probability weighting function vary significantly with (among other things) age, income, and wealth of the individual.     

Aspirations as reference points: an experimental investigation of risk behavior over time

This paper examines the importance of aspirations as reference points in a multi-period decision-making context. After stating their personal aspiration level, 172 individuals made six sequential decisions among risky prospects as part of a choice experiment. The results show that individuals make different risky-choices in a multi-period compared to a single-period setting. In particular, individuals’ aspiration level is their main reference point during the early stages of decision-making, while their starting status (wealth level at the start of the experiment) becomes the central reference point during the later stages of their multi-period decision-making.     

Social comparison and risky choices

Theories (and experiments) on decision making under risk typically ignore (and exclude) a social context. We explore whether this omission is detrimental. To do so we experimentally investigate the simplest possible situation with both social comparison and risk: participants choose between two lotteries while a referent faces a fixed payoff. Participants are more risk averse when they can earn at most as much as their referent (loss situation) than when they are ensured they will earn at least as much as their referent (gain situation). Prospect theory with a social reference point would predict the exact opposite behavior. These results show that straightforward extensions of existing theories to allow for social comparison do not provide accurate predictions.     

Gender differences in ambiguity aversion under different outcome correlation structures

This paper studies the impact of different outcome correlation structures on gender differences in ambiguity aversion. We conducted an investment game with two separate treatments. In the uncorrelated treatment, the outcomes of the investment game were determined individually. In the correlated treatment, the outcomes of the investment game were determined collectively within a reference group. From an evolutionary perspective, men should be more concerned about relative outcomes, because their reproductive success mainly depended on their relative standing within society. Women, by contrast, should be more concerned about absolute outcomes, because their reproductive success was mainly linked to their access to resources for themselves and their children. Therefore, we predict that the type of outcome correlation structure has a larger impact on men than on women. In particular, we hypothesize that men are less ambiguity averse under an uncorrelated outcome structure. In this situation, the ambiguous alternative should be more attractive, because it potentially reduces inequality and thereby improves men’s relative standing within society. Women’s choices should not be significantly affected by different outcome correlation structures. Both hypotheses are supported by evidence from laboratory experiments.     

Measuring risk aversion with lists: a new bias

Various experimental procedures aimed at measuring individual risk aversion involve a list of pairs of alternative prospects. We first study the widely used method by Holt and Laury (Am Econ Rev 92(5):1644–1655, 2002), for which we find that the removal of some items from the lists yields a systematic decrease in risk aversion and scrambles the ranking of individuals by risk aversion. This bias, that we call embedding bias, is quite distinct from other confounds that have been previously observed in the use of the HL method. It may be related to empirical phenomena and theoretical developments where better prospects increase risk aversion. Nevertheless, we also find that the more recent elicitation method due to Abdellaoui et al. (Theory Decis 71:63–80, 2011), also based on lists but using only one and the same probability in the list, does not display any statistically significant bias when the corresponding items of the list are removed. Our results suggest that methods other than the popular HL one may be preferable for the measurement of risk aversion.     

Prospect theory and the “forgotten” fourfold pattern of risk preferences

Markowitz (Journal of Political Economy 60:151–158, 1952) identified a fourfold pattern of risk preferences in outcome magnitude: When outcomes are large, people are risk averse in gains and risk seeking in losses, but risk preferences reverse when the outcomes are small, with people exhibiting risk seeking in gains and risk aversion in losses. This fourfold pattern was not addressed by either version of prospect theory (Kahneman and Tversky Econometrica 47:363–391, 1979; Tversky and Kahneman Journal of Risk and Uncertainty 5:297–323, 1992). We show how prospect theory can accommodate the pattern by combining an overweighting of low probabilities with a decreasingly elastic value function. We then examine the performance of prospect theory with two decreasingly elastic value functions: Prospect theory performs better, both quantitatively and qualitatively, with a normalized logarithmic value function than with a normalized exponential value function. We discuss several issues, and speculate about why Tversky and Kahneman did not address Markowitz’s fourfold pattern.