Dynamics of Sequential Decision Making

We suggest a new paradigm for intelligent decision-making suitable for dynamical sequential activity of animals or artificial autonomous devices that depends on the characteristics of the internal and external world. To do it we introduce a new class of dynamical models that are described by ordinary differential equations with a finite number of possibilities at the decision points, and also include rules solving this uncertainty. Our approach is based on the competition between possible cognitive states using their stable transient dynamics. The model controls the order of choosing successive steps of a sequential activity according to the environment and decision-making criteria. Two strategies (high-risk and risk-aversion conditions) that move the system out of an erratic environment are analyzed.

Figure 1

A sequence of cognitive states: thin lines, possible paths; thick line, realized sequence chosen by the DM according to information fro the environment; $t_3$, $t_4$, $t_6$, $t_9$ are instants of choices.

Figure 2

High-risk DM dynamics of a system with $N=20$ and $M=5$: (a) Most commonly observed DM behavior. (b) An example of the repetitive decisions that can be found in a system with repetitive environment and small percentage of uncertainty. Different tones represent different $a_i$.

Figure 3

Phase transition for the high-risk DM. Median of the length of life $L$ (dashed lines) and median of the number of nodes involved in the sequence (solid lines) versus the number of choices $M$ for the CSM with numbers cognitive states: $N=10$, 25, 50.

Figure 4

Probability of finding a sequence of length $L$ as a function of the size of the system $N=75$ for the risk-aversion DM function. $M=5$, 10, 15 are used in this figure. All of the curves for different $M$ are on top of each other. We do not display the median here because there is no phase transition unlike in Fig. 3.