A Catastrophe Model for the Prospect-Utility Theory Question

Terence A. Oliva, Temple University, Philadelphia, PA

Sean R. McDade, PeopleMetics (TM) Philadelphia, PA

**Abstract: **Anomalies have played a big part in the analysis of decision making under risk.
Both expected utility and prospect theories were born out of anomalies exhibited by actual
decision making behavior. Since the same individual can use both expected utility and prospect
approaches at different times, it seems there should be a means of uniting the two. This paper
turns to nonlinear dynamical systems (NDS), specifically a catastrophe model, to help suggest
an ”out of the box” line of solution toward integration. We use a cusp model to create a
value surface whose control dimensions are involvement and gains versus losses.
By including ”involvement” as a variable the importance of the individual”s psychological
state is included, and it provides a rationale for how decision makers” changes from
expected utility to prospect might occur. Additionally, it provides a possible
explanation for what appears to be even more irrational decisions that individuals
make when highly emotionally involved. We estimate the catastrophe model using a
sample of 997 gamblers who attended a casino and compare it to the linear model using
regression. Hence, we have actual data from individuals making real bets, under real conditions.

*Keywords: *catastrophe theory, decision theory, nonlinear dynamics, prospect theory, risk aversion