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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)

Pascal’s wager is one of the most influential arguments in philosophy and decision theory. This paper reformulates Pascal’s wager in terms of two-outcome finite payoffs (one before death and one af...

We collected 299 frontal face images of 2017 cabinet ministers from 15 post‐Soviet states (Armenia, Azerbaijan, Belarus, Estonia, Georgia, Kazakhstan, Kyrgyzstan, Latvia, Lithuania, Moldova, Russia, Tajikistan, Turkmenistan, Ukraine and Uzbekistan). For each image, the minister's body‐mass index is estimated using a computer vision algorithm. The median estimated body‐mass index of cabinet ministers is highly correlated with conventional measures of corruption (Transparency International Corruption Perceptions Index, World Bank worldwide governance indicator Control of Corruption, Index of Public Integrity). This result suggests that physical characteristics of politicians such as their body‐mass index can be used as proxy variables for political corruption when the latter are not available, for instance at a very local level.

In the television show Affari Tuoi a contestant is endowed with a sealed box containing a monetary prize between one cent and half a million euros. In the course of the show the contestant learns more information about the distribution of possible monetary prizes inside her box. Consider two groups of contestants, who learned that the chances of their boxes containing a large prize are 20% and 80% correspondingly. Contestants in both groups receive qualitatively similar price offers for selling the content of their boxes. If contestants are less risk averse when facing unlikely gains, the price offer is likely to be more frequently rejected in the first group than in the second group. However, the fraction of rejections is virtually identical across two groups. Thus, contestants appear to have identical risk attitudes over (large) gains of low and high probability.

Unlike the Nash equilibrium, logit quantal response equilibrium is affected by positive affine transformations of players’ von Neumann–Morgenstern utility payoffs. This paper presents a modification of a logit quantal response equilibrium that makes this equilibrium solution concept invariant to arbitrary normalization of utility payoffs. Our proposed modification can be viewed as a refinement of logit quantal response equilibria: instead of obtaining a continuum of equilibria (for different positive affine transformations of utility function) we now obtain only one equilibrium for all possible positive affine transformations of utility function. We define our refinement for simultaneous-move noncooperative games in the normal form.

The Allais Paradox, or Common Consequence Effect to be precise, is one of the most wellknown behavioral regularities in individual decision making under risk. A common perception in the literature, which motivated the development of numerous generalized non‐expected utility theories, is that the Allais Paradox is a robust empirical finding. We argue that such a perception does not accurately reflect the experimental evidence on the Allais Paradox and show how specific choices of parameters can make it appear, disappear, or reverse. For example, our results suggest that the Allais Paradox is likely to disappear when lotteries involve relatively small outcomes under real financial incentives and probability distributions are described as compound lotteries or in a frequency format (rather than as reduced‐form simple lotteries). We also find that the Allais Paradox is likely to get reversed when lotteries are designed with an even division of the probability mass between the lowest and the highest outcomes.

This paper studies coordination in a multi-stage elimination tournament with large monetary incentives and a diversified subject pool drawn from the adult British population. In the tournament, members of an ad hoc team earn money by answering general knowledge questions and then eliminate one contestant by plurality voting without prior communication. We find that in the early rounds of the tournament, contestants use a focal principle and coordinate on one of the multiple Nash equilibria in pure strategies by eliminating the weakest member of the team. However, in the later rounds, contestants switch to playing a mixed strategy Nash equilibrium.

Economic research offers two traditional ways of analyzing decision making under risk. One option is to compare the goodness of fit of different decision theories using the same model of stochastic choice. An alternative way is to vary models of stochastic choice combining them with only one or two decision theories. This paper proposes to look at the bigger picture by comparing different combinations of decision theories and models of stochastic choice. We select a menu of seven popular decision theories and embed each theory in five models of stochastic choice including tremble, Fechner and random utility model. We find that the estimated parameters of decision theories differ significantly when theories are combined with different models. Depending on the selected model of stochastic choice we obtain different ranking of decision theories with regard to their goodness of fit to the data. The fit of all analyzed decision theories improves significantly when they are embedded in a Fechner model of heteroscedastic truncated errors (or random utility model in a dynamic decision problem).

In the television show Affari Tuoi a contestant is endowed with a sealed box containing a monetary prize between one cent and half a million euros. In the course of the show the contestant is offered to exchange her box for another sealed box with the same distribution of possible monetary prizes inside. This offers a unique natural laboratory for testing the predictions of expected utility theory versus prospect theory using lotteries with large stakes. While expected utility theory predicts that an individual is exactly indifferent between accepting and rejecting the exchange offer, prospect theory predicts that an individual should always reject the exchange offer due to the assumption of loss aversion. We find that the assumption of loss aversion is violated by 46 percent of all contestants in our recorded sample. Thus, contestants do not appear to be predominantly loss averse when dealing with lotteries involving large stakes.

In the television show Affari Tuoi an individual faces a sequence of binary choices between a risky lottery with equiprobable prizes of up to half a million euros and a monetary amount for certain. The decisions of 114 show participants are used to test the predictions of ten decision theories: risk neutrality, expected utility theory, fanning-out hypothesis (weighted utility theory, transitive skew-symmetric bilinear utility theory), (cumulative) prospect theory, regret theory, rank-dependent expected utility theory, Yaari�s dual model, prospective reference theory and disappointment aversion theory. Assumptions of risk neutrality and loss aversion are clearly violated, respectively, by 55% and 46% of all contestants. There appears to be no evidence of nonlinear probability weighting or disappointment aversion. Observed decisions are generally consistent with the assumption of regret aversion and there is strong evidence for the fanning-out hypothesis. Nevertheless, we find no behavioral patterns that cannot be reconciled within the expected utility framework (or prospective reference theory that gives identical predictions).

Conventional parameterizations of cumulative prospect theory do not explain the St. Petersburg paradox. To do so, the power coefficient of an individual's utility function must be lower than the power coefficient of an individual's probability weighting function.

In binary choice between discrete outcome lotteries, an individual may prefer lottery L1 to lottery L2 when the probability that L1 delivers a better outcome than L2 is higher than the probability that L2 delivers a better outcome than L1. Such a preference can be rationalized by three standard axioms (completeness, continuity and first order stochastic dominance) and two less standard ones (weak independence and a fanning-in). A preference for the most probable winner can be represented by a skew-symmetric bilinear utility function. Such a utility function has the structure of a regret theory when lottery outcomes are perceived as ordinal and the assumption of regret aversion is replaced with a preference for a win. The empirical evidence supporting the proposed system of axioms is discussed.

The optimal contest architecture for symmetric imperfectly discriminating contests is shown to be generically the two-stage tournament (rather than the one-stage contest). In the first stage the contestants compete in several parallel divisions for the right to participate in the second stage. In the second stage the short-listed finalists compete for the prize. Given a sufficient number of contestants, the two-stage tournament is either strictly better or at least as good as the one-stage contest for maximizing an individual�s effort, for maximizing the aggregate effort and for minimizing the standard deviation of effort. For maximizing an individual�s effort it is generally optimal to have only two finalists in the second stage. For maximizing the aggregate effort or minimizing the standard deviation of effort the optimal number of finalists in the second stage depends on the discriminating power of the contest success function.

Elicitation methods in decision making under risk allow a researcher to infer the subjective utilities of outcomes as well as the subjective weights of probabilities from the observed preferences of an individual. An optimally efficient elicitation method is proposed, which takes into account the inevitable distortion of preferences by random errors and minimizes the effect of such errors on the inferred utility and probability weighting functions. Under mild assumptions, the optimally efficient method for eliciting utilities (weights) of many outcomes (probabilities) is the following three-stage procedure. First, a probability is elicited whose subjective weight is one half. Second, an individual�s utility function is elicited through the midpoint chaining certainty equivalent method employing the probability elicited at the first stage as an input. Finally, an individual�s probability weighting function is elicited through the probability equivalent method.

When the performance of a risky asset is frequently assessed, the probability of detecting a loss is high, which averts the loss averse investors. This effect is known as myopic loss aversion (MLA). This paper reexamines several recent experimental studies documenting the existence of MLA. A closer look at the experimental data reveals that the effect of MLA is largely neutralized by the overweighting of small probabilities and the underweighting of moderate and high probabilities. Remarkably, the two effects exactly balance each other out for conventional parameterizations of cumulative prospect theory. MLA alone cannot explain the observed investment decisions.

In imperfectly discriminating contests the contestants contribute effort to win a prize but the highest contributed effort does not necessarily secure a win. The contest success function (CSF) is the technology that translates an individual�s effort into his or her probability of winning. This paper provides an axiomatization of CSF when there is the possibility of a draw (the sum of winning probabilities across all contestants is non-additive)..

There are at least two reasons why multiple prizes can be optimal in symmetric imperfectly discriminating contests. First, the introduction of multiple prizes reduces the standard deviation of contestants� effort in asymmetric equilibria, when the majority of contestants actively participate in competition. Second, the introduction of multiple prizes may increase the aggregate (average) effort contributed in the contest. When more of a total prize fund is shifted away from the first prize, on the one hand, the active contestants obtain an incentive to reduce their individual effort, but, on the other hand, the number of active contestants may increase. Therefore, the aggregate (average) effort may increase when the number of active contestants in equilibrium increases.