Gambling and nonexpected utility: the perils of the power function

Abstract

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.

Notes

¹ The model can explain a variety of experimental evidence seemingly inconsistent with expected utility theory, see e.g. Allais and Hagen (1979), Rabin (2000). Also Cain et al (2005) for more on cumulative prospect theory and gambling.

² In particular the favourite longshot bias see e.g. Golec and Tamarkin (1998).

³ Also see Aloysius (2003).

⁴ Since wealth can be defined quite generally as one unit, small can be defined relative to wealth.

⁵ Using the form in Prelec (1998) makes no qualitative difference to the results.