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The aim of this paper is to propose a behavioral characterization of individuals who underestimate probabilities modifications and to characterize this behavior in the standard preferences representation models under risk (expected utility, dual theory, rank dependent utility theory and MaxMin expected utility). Our main results are the following. Underreaction to probabilities modifications is in general independent from standard risk aversion and prudence. In models involving probabilities transformation functions, it is characterized by the slope of the probability transformation function. In the MaxMin expected utility model under risk, it is related to the weights of the maximal and minimal consequences in the preferences representation function. Considering a simple prevention decision, consisting in the reduction in the probability of a monetary loss, we show that individuals who underreact to probabilities modifications, invest less in prevention than individuals who objectively evaluate these modifications. Underreaction to probabilities modification is thus a possible explanation for low investment in prevention.

This paper characterizes the optimal way for a principal to structure a rank-order tournament in a moral hazard setting (as in Lazear and Rosen (1981)). We find that it is generally optimal to give rewards to top performers that are smaller in magnitude than corresponding punishments to poor performers. The paper identifies four reasons why the principal might prefer to give larger rewards than punishments: (i) R is small relative to P (where R is risk aversion and P is absolute prudence); (ii) the distribution of shocks to ouput is asymmetric and the asymmetry takes a particular form; (iii) the principal faces a limited liability constraint; and (iv) there is agent heterogeneity of a particular form. An intuition is given as to why these factors affect the optimal prize schedule. Using the theory developed by Green and Stokey (1983), we relate the results about tournaments to the structure of the optimal individual contract. The optimal individual contract typically punishes low output more than it rewards high output. We also give conditions under which the optimal individual contract will be a concave function of output.

This note provides an alternative proof for the equivalence of decreasing absolute prudence (DAP) in the expected utility framework and in a two-parametric approach where utility is a function of the mean and the standard deviation. In addition, we elucidate that the equivalence of DAP and the concavity of utility as a function of mean and variance, which was shown to hold for normally distributed stochastics in Lajeri and Nielsen [Economic Theory 15 (2000), 469-476], cannot be generalized.

In this note we use the rank-dependent utility (RDU) model to analyze saving decisions. The RDU model enables us to separate the effects of pessimism and optimism on saving from that of concavity of the utility function. While pessimism induces more saving, the importance of this effect is shown to depend upon properties of the utility function such as prudence and temperance.