Hypothetical Payoffs Research Articles

On the Experimental Robustness of the Allais Paradox

The Allais Paradox, or the common consequence effect, is a well-known behavioral regularity in individual decision-making under risk. Data from 81 experiments reported in 29 studies reveal that the Allais Paradox is a fragile empirical finding. The Allais Paradox is likely to be observed in experiments with high hypothetical payoffs, the medium outcome being close to the highest outcome and when lotteries are presented as a probability distribution (not in a compound form). The Allais Paradox is likely to be reversed in experiments when the probability mass is equally split between the lowest and highest outcomes in risky lotteries. (JEL D44, D81)

Do as I Do, Not as I Say: Incentivization and the Relationship Between Cognitive Ability and Risk Aversion

We study how the use of real and hypothetical choices to elicit risk preferences affect the statistical relationship between cognitive ability and risk aversion. Our experimental results suggest that such association is sensitive to incentive conditions of the choice problems used to elicit risk preferences. Individuals in the upper tail of the cognitive ability distribution are willing to take more risks. But this holds only when choices involve hypothetical payoffs. When choices are real, this correlation is found insignificant. Results are robust to using alternative measures of cognitive ability.

A model for the evolution of reinforcement learning in fluctuating games

Many species are able to learn to associate behaviours with rewards as this gives fitness advantages in changing environments. Social interactions between population members may, however, require more cognitive abilities than simple trial-and-error learning, in particular the capacity to make accurate hypotheses about the material payoff consequences of alternative action combinations. It is unclear in this context whether natural selection necessarily favours individuals to use information about payoffs associated with nontried actions (hypothetical payoffs), as opposed to simple reinforcement of realized payoff. Here, we develop an evolutionary model in which individuals are genetically determined to use either trial-and-error learning or learning based on hypothetical reinforcements, and ask what is the evolutionarily stable learning rule under pairwise symmetric two-action stochastic repeated games played over the individual's lifetime. We analyse through stochastic approximation theory and simulations the learning dynamics on the behavioural timescale, and derive conditions where trial-and-error learning outcompetes hypothetical reinforcement learning on the evolutionary timescale. This occurs in particular under repeated cooperative interactions with the same partner. By contrast, we find that hypothetical reinforcement learners tend to be favoured under random interactions, but stable polymorphisms can also obtain where trial-and-error learners are maintained at a low frequency. We conclude that specific game structures can select for trial-and-error learning even in the absence of costs of cognition, which illustrates that cost-free increased cognition can be counterselected under social interactions.

Differences in cognitive control between real and hypothetical payoffs

This study focuses on the question of neural differences in the evaluation of hypothetical and real payoffs. Hypothetical payoffs are not incentive compatible and are, therefore, not considered to be reliable. Behavioral differences between the evaluation of hypothetical and real payoffs can be attributed to this incentive effect. Because real payoff mechanisms are not always applicable in the field, it is necessary to know in which way both types of payoffs affect evaluation processes. In order to delineate the cognitive processes related to hypothetical bias, we conducted a within-subject EEG experiment with hypothetical and real payoffs. A certainty equivalent elicitation method for measuring risk attitudes was performed in which subjects had to indicate whether they preferred playing a lottery or receiving a sure payoff instead. At the behavioral level, subjects were more risk averse for real payoff choices, confirming a hypothetical bias. EEG-derived event-related potentials provide evidence that the processes underlying these differences in evaluations differ. A higher N2 component for hypothetical payoffs revealed increased cognitive control for hypothetical decisions. These neuronal underpinnings indicate additional evaluation processes in hypothetical choice paradigms, which can explain the shift in risk attitude toward the expected value of a lottery.

Framing Influences Willingness to Pay but Not Willingness to Accept

The authors show, with real and hypothetical payoffs, that consumers are willing to pay substantially less for a risky prospect when it is called a “lottery ticket,” “raffle,” “coin flip,” or “gamble” than when it is labeled a “gift certificate” or “voucher.” Willingness to accept, in contrast, is not affected by these frames. This differential framing effect is the result of an aversion to bad deals, which causes buyers to focus on different aspects than sellers. Buyers’ willingness to pay is influenced by the extent to which a risky prospect's frame is associated with risk (Experiment 1) as well as the prospect's lowest (but not highest) possible outcome (Experiment 2). Sellers’ willingness to accept, in contrast, is influenced by a prospect's lowest and highest possible outcomes but not by the risk associated with its frame (Experiments 2 and 3). The framing effect on willingness to pay is independent of the objective level of uncertainty (Experiment 4) and can lead to the uncertainty effect. The findings have important implications for research on risk preferences and marketing practice.

Tensions that Make a Difference: Institutions, Interests, and the Immigrant Drive1

This article examines the dynamics underlying contemporary South‐North population displacements and the common gaps between public perceptions of the phenomenon and actual realities. I analyze these dynamics and gaps by focusing on the clash between opposing forces at various stages of the migration process. These tensions occur between actors endowed with unequal power, leading to inefficient Nash‐like equilibria where the interests of less powerful participants and those of society‐at‐large in the successful integration of its newest members are not maximized. Matrices of hypothetical payoffs for relevant actors are presented for illustration. Systemic changes that would alter the present situation in the direction of more efficient and stable outcomes are discussed.

Allais for all: Revisiting the paradox in a large representative sample

We administer the Allais paradox questions to both a representative sample of the Dutch population and to student subjects. Three treatments are implemented: one with the original high hypothetical payoffs, one with low hypothetical payoffs and a third with low real payoffs. Our key findings are: (i) violations in the non-lab sample are systematic and a large bulk of violations is likely to stem from non-familiarity with large payoffs, (ii) we can identify groups of the general population that have much higher than average violation rates; this concerns mainly the lowly educated and unemployed, and (iii) the relative treatment differences in the population at large are accurately predicted by the lab sample, but violation rates in all lab treatments are about 15 percentage points lower than in the corresponding non-lab treatments.

Physiological Plausibility and Boundary Conditions of Theories of Risk Sensitivity

The contribution by Yechiam and Telpaz (Y&T) published in Frontiers in Cognitive Science places it in a corpus of literature which bridges at least three different disciplines, i.e., psychology, economics, and neuroscience. The goal of this line of research is to explore the neurological and physiological underpinnings of one of the central topics in judgment and decision-making (JDM) research – choice behavior in decisions from experience. Y&T successfully contributes to this goal by demonstrating a novel effect that losses increase experimental participants’ arousal as measured by pupil dilatation, which in turn positively correlates with a risk aversion behavior. They hypothesize that participants’ attention is increased in decision problems involving losses, which trigger an innate prudent behavior in situations entailing danger and/or hazard. Interestingly, Y&T find that the nature of attention is not selective, i.e., when losses are present, participants are shown to devote more attention to the task as a whole rather than to the single negative outcomes, in contrast to Prospect Theory's loss aversion. YT Tom et al., 2007). These studies suggest that behavioral loss aversion in decisions from description reflects an asymmetric response to gain and losses in the neural system encoding for reward values (the ventromedial prefrontal cortex, orbitofrontal cortex, and ventral striatum). What makes Y&T's contribution particularly noteworthy is their mediating attentional hypothesis, which links physiological mechanisms to the psychological processes involved in experience-based decisions. One of the possible future developments from YT Holt and Laury, 2005). Specifically, it has been observed that participants’ degree of risk aversion increases significantly as actual positive payoffs are scaled up, and that this effect is negligible when payoffs are hypothetical. These findings provide an opportunity to widen the scope of the attentional hypothesis. Specifically, payoffs corresponding to large cash amounts might have the analogous effects of losses of increasing arousal and of triggering a higher level of risk aversion; whereas hypothetical payoffs might result in a substantial inhibition of attention. Therefore, the motivation implied by real stakes can be interpreted as one of the possible boundary conditions (see below) for Y&T's attentional hypothesis, giving rise to a question of the relative weight of attention and motivation in shaping risk attitudes. Y&T's report can also be contextualized within the wide literature on individual differences in reasoning, judgment and decision making (e.g., Stanovich and West, 2000) and their implications to the rationality debate. The prototypical finding in that literature is the correlation between cognitive ability and normative responding, with a strong emphasis on normative evaluation of rationality. This so-called “normativist” approach has recently been subject to criticism (Elqayam and Evans, 2011) as unhelpful in developing a psychological theory of human rationality. It is therefore noteworthy that Y&T take their individual differences work in a completely different direction, with what seems to be a purely ‘descriptivist’ approach, with no normativist connotations. As one reviewer of this manuscript put it, any behavior in this setting could be justified as ‘rational’. The behavioral patterns described vary qualitatively rather than quantitatively. This is typical of descriptivist approaches to cognitive variability higher mental processing (Evans and Elqayam, 2011). Given the dearth of such focus in higher mental processing, this is a welcome development. Lastly, a potentially significant issue here is the implications to risk aversion as originally portrayed in prospect theory (Kahneman and Tversky, 1979). One could argue that Y&T contribute to defining boundary conditions for Prospect Theory, by proposing an alternative explanation for specific settings in which Prospect Theory is not supported by empirical evidence1. Indeed, as a unified theory of risk aversion is not yet at hand, knowing the range of application of each of the existing theories is crucial. One reason that YT the algorithmic level, which has to do with processes (e.g., the calculator's software); and the implementational level, which explores the physical underpinnings of the system – its hardware/wetware characterization (e.g., the calculator's chip). Viewed in these terms, we see prospect theory as portraying behavior mainly on the computational (i.e., functional) level of analysis; or, as some authors put it – an “axiomatic” system (see Wakker, 2010). In contrast, YT Tom et al., 2007), and studies that combine several levels of analysis, as Y&T have done, are even rarer. This makes Y&T's contribution of particular interest to scholars of human thinking and decision making.

Distributed Coding of Actual and Hypothetical Outcomes in the Orbital and Dorsolateral Prefrontal Cortex

Knowledge about hypothetical outcomes from unchosen actions is beneficial only when such outcomes can be correctly attributed to specific actions. Here we show that during a simulated rock-paper-scissors game, rhesus monkeys can adjust their choice behaviors according to both actual and hypothetical outcomes from their chosen and unchosen actions, respectively. In addition, neurons in both dorsolateral prefrontal cortex and orbitofrontal cortex encoded the signals related to actual and hypothetical outcomes immediately after they were revealed to the animal. Moreover, compared to the neurons in the orbitofrontal cortex, those in the dorsolateral prefrontal cortex were more likely to change their activity according to the hypothetical outcomes from specific actions. Conjunctive and parallel coding of multiple actions and their outcomes in the prefrontal cortex might enhance the efficiency of reinforcement learning and also contribute to their context-dependent memory.

Loss-aversion and household portfolio choice

In this paper we empirically test if loss-aversion affects household participation in equity markets, household allocations to equity, and household allocations between mutual funds and individual stocks. Using household survey data, we obtain direct measures of each surveyed household's loss-aversion coefficient from questions involving hypothetical payoffs. We find that higher loss-aversion is associated with a lower probability of participation. We also find that higher loss-aversion reduces the probability of direct stockholding by significantly more than the probability of owning mutual funds. After controlling for sample selection we do not find a relationship between loss-aversion and portfolio allocations to equity.

Loss-Aversion and Household Portfolio Choice

In this paper we empirically test if loss-aversion affects household participation in equity markets, household allocations to equity, and household allocations between mutual funds and individual stocks. Using household survey data, we obtain direct measures of each surveyed household’s loss-aversion coefficient from questions involving hypothetical payoffs. We find that higher loss-aversion is associated with a lower probability of participation. We also find that higher loss-aversion reduces the probability of direct stockholding by significantly more than the probability of owning mutual funds. After controlling for sample selection we do not find a relationship between loss-aversion and portfolio allocations to equity.

ON THE LINKAGE BETWEEN FINANCIAL RISK TOLERANCE AND RISK AVERSION

AbstractWe explore the linkage between financial risk tolerance (FRT) and risk aversion. To do this, we obtain FRT scores from a psychometrically validated survey and conduct a battery of online lottery choice experiments involving the same nonstudent participants. We contrast: real and hypothetical payoffs, low and high stakes, decisions involving gains and losses, and order effects. Our key finding is that the two approaches to analyzing decision making under uncertainty are strongly aligned. We present evidence that this is particularly the case for the female participants in our sample and when high‐stake gambles are employed.

A shocking experiment: New evidence on probability weighting and common ratio violations

AbstractWe study whether probability weighting is observed when individuals are presented with a series of choices between lotteries consisting of real non-monetary adverse outcomes, electric shocks. Our estimation of the parameters of the probability weighting function proposed by Tversky and Kahneman (1992) are similar to those obtained in previous studies of lottery choice for negative monetary payoffs and negative hypothetical payoffs. In addition, common ratio violations in choice behavior are widespread. Our results provide evidence that probability weighting is a general phenomenon, independent of the source of disutility.

On the Linkage between Financial Risk Tolerance and Risk Aversion: Evidence from a Psychometrically-Validated Survey versus an Online Lottery Choice Experiment

There are two related literatures on financial risk tolerance (FRT) (based on psychometrically-validated surveys) and risk aversion (based on lottery experiments) that hitherto have not been intersected. Exploring their integration is the primary goal of this paper. Specifically, we follow a two stage process: (1) we obtain FRT scores from a psychometrically-validated survey on a sample of 162 people; and (2) we conduct a battery of lottery choice experiments on the same people. The second stage is primarily distinguished from earlier lottery choice experiments by being online and involving non-student subjects. Moreover, we contrast: real and hypothetical payoffs; low and high stake payoffs; decisions involving gains and losses; and order effects. Our key finding is that the two approaches to analysing decision-making under uncertainty are strongly aligned. We present evidence that this is particularly the case for the female participants in our sample. There is also some evidence that the alignment is strengthened when high stake gambles are employed.

Learning and decision making in monkeys during a rock–paper–scissors game

Game theory provides a solution to the problem of finding a set of optimal decision-making strategies in a group. However, people seldom play such optimal strategies and adjust their strategies based on their experience. Accordingly, many theories postulate a set of variables related to the probabilities of choosing various strategies and describe how such variables are dynamically updated. In reinforcement learning, these value functions are updated based on the outcome of the player's choice, whereas belief learning allows the value functions of all available choices to be updated according to the choices of other players. We investigated the nature of learning process in monkeys playing a competitive game with ternary choices, using a rock–paper–scissors game. During the baseline condition in which the computer selected its targets randomly, each animal displayed biases towards some targets. When the computer exploited the pattern of animal's choice sequence but not its reward history, the animal's choice was still systematically biased by the previous choice of the computer. This bias was reduced when the computer exploited both the choice and reward histories of the animal. Compared to simple models of reinforcement learning or belief learning, these adaptive processes were better described by a model that incorporated the features of both models. These results suggest that stochastic decision-making strategies in primates during social interactions might be adjusted according to both actual and hypothetical payoffs.

Effects of Presentation Order on Product Evaluation: An Empirical Analysis

There are a number of consumer behaviour theories regarding the importance of the first stimulus and of a reference point in buying decision-making. However, there are not many empirical analyses, and they usually consider only hypothetical situations and payoffs. This paper aims to fill the gap by providing an empirical analysis for the effects of presentation order, using data collected in a natural setting. Two different personal computers are considered and evaluated along with the perceptions of price, quality, and price–quality relationship; evaluations are compared when the presentation order changes. The results confirm that the first alternative is more likely to be preferred; however, presentation order effects are not the same for all elements and show a relative rigidity for price perception. Managerial implications and issues for future research are highlighted.

Why use real and hypothetical payoffs?

Decision making can be studied using hypothetical payoffs because it is hypothetical to its very core. However, the core process can be influenced by contextual features. As there is no theory for these contextual features, a “do-it-both-ways” rule amounts to a waste of money. If we had such a theory, doing it both ways would be unnecessary.

Varying the scale of financial incentives under real and hypothetical conditions

The use of high hypothetical payoffs has been justified by the realism and relevance of large monetary consequences and by the impracticality of making high cash payments. We argue that subjects may not be able to imagine how they would behave in high payoff situations.

Hypothetical and real consequences in experimental auctions for insurance against low‐probability risks

AbstractLaboratory experiments have provided useful information about how people behave in risky situations. In particular, such experiments have allowed for the observation of many deviations from the predictions of expected utility theory. There is some dispute, however, over the effect of the use of real versus hypothetical money in these experiments and over the impact of experience. In this paper we describe auction experiments in which subjects faced a low‐probability risk with either hypothetical or real‐money consequences and varying amounts of experience. Using hypothetical payoffs resulted in behavior that provides a reasonable qualitative prediction of behavior with real consequences, but that seems to indicate a less diligent altitude toward spending the money as well as less concern about the risk.

Realism and Risk Taking

Ss made decisions on a questionnaire for real payoffs and for hypothetical payoffs. They tended to be less risky when their decisions were made for real consequences than when their decisions were hypothetical, suggesting that one should be cautious in predicting real risk-taking behavior from measures of hypothetical risk.