Gambling and nonexpected utility: the perils of the power function

The use of the power utility function is problematic in expected utility theory. We show that, this is also the case in cumulative prospect theory, where the power function violates the assumption of loss-aversion at small stake levels, so that an optimal model of gambling is precluded. In the case of rank-dependent expected utility it has the counterfactual implication that agents will gamble all of their wealth at actuarially unfair odds.