Stronger Utility

Empirical research often requires a method how to convert a deterministic economic theory into an econometric model. A popular method is to add a random error term on the utility scale. This method, however, violates stochastic dominance. A modification of this method is proposed to avoid violations of dominance. The modified model compares favorably to other existing models in terms of goodness of fit to experimental data. The modified model can rationalize the preference reversal phenomenon. An intuitive axiomatic characterization of the modified model is provided. Important microeconomic concept of risk aversion is well-defined in the modified model.Decision Theory, Probabilistic Choice, Stochastic Dominance, Strong Utility, Risk Aversion

Betting on own knowledge: Experimental test of overconfidence

This paper presents a new incentive compatible method for measuring confidence in own knowledge. This method consists of two parts. First, an individual answers several general knowledge questions. Second, the individual chooses among three alternatives: (1) one question is selected at random and the individual receives a payoff if he or she has answered this question correctly; (2) the individual receives the same payoff with a probability equal to the percentage of correctly answered questions; (3) either the first or the second alternative is selected. The choice of the first (second) alternative reveals overconfidence (underconfidence). The individual is well calibrated if he or she chooses the third alternative. Experimental results show that subjects, on average, exhibit underconfidence about their own knowledge when the incentive compatible mechanism is used. Their confidence in own knowledge does not depend on their attitude towards risk/ambiguit

Coordination, focal points and voting in strategic situations : a natural experiment

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

Axiomatization of a Preference for Most Probable Winner

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 (solvability, convexity and symmetry) and one less standard axiom (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 discusse

Error Propagation in the Elicitation of Utility and Probability Weighting Functions

Elicitation methods in decision-making under risk allow us to infer the utilities of outcomes as well as the probability weights from the observed preferences of an individual. An optimally efficient elicitation method is proposed, which takes the inevitable distortion of preferences by random errors into account 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 and probability weights is the following three-stage procedure. First, a probability is elicited whose subjective weight is one half. Second, the utility function is elicited through the midpoint chaining certainty equivalent method using the probability elicited at the first stage. Finally, the probability weighting function is elicited through the probability equivalent metho

Stochastic expected utility theory

This paper proposes a new decision theory of how individuals make random errors when they compute the expected utility of risky lotteries. When distorted by errors, the expected utility of a lottery never exceeds (falls below) the utility of the highest (lowest) outcome. This assumption implies that errors are likely to overvalue (undervalue) lotteries with expected utility close to the utility of the lowest (highest) outcome. Proposed theory explains many stylized empirical facts such as the fourfold pattern of risk attitudes, common consequence effect (Allais paradox), common ratio effect and violations of betweenness. Theory fits the data from ten well-known experimental studies at least as well as cumulative prospect theor

Harmonic sequence paradox

Summary.: Informal evidence suggests that individuals are willing to pay only a finite and, typically, very low price for a specific lottery that converges to an infinite payment with probability one. The established decision theories (expected value, expected utility theory, cumulative prospect theory) cannot satisfactorily explain this low willingness to pay. The presented paradox strengthens the original and the super St. Petersburg parado

Risk Aversion when Gains are Likely and Unlikely: Evidence from a Natural Experiment with Large Stakes

In the television show Deal or No Deal a contestant is endowed with a sealed box, which potentially contains a large monetary prize. 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 probabilit

Endowment effects? "Even” with half a million on the table!

In the television show Deal or No Deal, 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 experiment for studying endowment effects under high monetary incentives. We find evidence of only a weak endowment effect when contestants exchange their box for another box with the same distribution of possible prize

Range effects and lottery pricing

A standard method to elicit certainty equivalents is the Becker-DeGroot-Marschak (BDM) procedure. We compare the standard BDM procedure and a BDM procedure with a restricted range of minimum selling prices that an individual can state. We find that elicited prices are systematically affected by the range of feasible minimum selling prices. Expected utility theory cannot explain these results. Non-expected utility theories can only explain the results if subjects consider compound lotteries generated by the BDM procedure. We present an alternative explanation where subjects sequentially compare the lottery to monetary amounts in order to determine their minimum selling price. The model offers a formal explanation for range effects and for the underweighting of small and the overweighting of large probabilitie