Modeling Risky Decision Making by Cellular Automata

This paper proposes a new approach to the problem of decision making under risk (and partly under uncertainty) by a simple cellular automaton which can simulates wellknown anomalies of risky choice. This field has been studied mainly by psychologists, economists, management scientists, and more recently neuroscientists so far. Various types of anomalous choice patterns which violate the prediction according to the probability theory and the expected utility theory are called paradoxes, or anomalies. Specifically, descriptive theory of risky choice should model the effects of event-splitting (and event-merging) to violate the first-order stochastic dominance, as well as the ambiguity aversion and the common consequence effect. By editing branches and matching of rows in two gambles, one could invite anomalous choice which reverses mathematically the same choice, therefore decision maker’s risk cognition permit a manipulation by the problem representation. Figure 1 and Figure 2 show examples (They are the choice problems 2 and 3.2 in Birnbaum (2008)).